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 Page 1


Newton’s Laws of Motion
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 First Law of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.1 Example 5.1 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.2 Inertial Frames Other Than Earth . . . . . . . . . . . . . . . . . . . . . . . 3
3 Second Law of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
3.1 Example 5.2 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
4 Working with Newton’s First and Second Laws . . . . . . . . . . . . . . . . . 3
4.1 Example 5.3 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
5 Third Law of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
5.1 Example 5.4 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
5.2 Working with Tension in a String . . . . . . . . . . . . . . . . . . . . . . . 5
5.3 Example 5.5 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
6 Pseudo Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
7 The Horse and the Cart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
8 Inertia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
9 Worked Out Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
9.1 Worked Out Example 1 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . 6
9.2 Worked Out Example 2 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . 6
9.3 Worked Out Example 3 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . 7
9.4 Worked Out Example 4 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . 7
9.5 Worked Out Example 5 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . 7
9.6 Worked Out Example 6 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . 7
9.7 Worked Out Example 7 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . 7
9.8 Worked Out Example 8 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . 8
9.9 Worked Out Example 9 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . 8
9.10 Worked Out Example 10 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . 8
1
Page 2


Newton’s Laws of Motion
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 First Law of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.1 Example 5.1 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.2 Inertial Frames Other Than Earth . . . . . . . . . . . . . . . . . . . . . . . 3
3 Second Law of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
3.1 Example 5.2 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
4 Working with Newton’s First and Second Laws . . . . . . . . . . . . . . . . . 3
4.1 Example 5.3 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
5 Third Law of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
5.1 Example 5.4 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
5.2 Working with Tension in a String . . . . . . . . . . . . . . . . . . . . . . . 5
5.3 Example 5.5 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
6 Pseudo Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
7 The Horse and the Cart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
8 Inertia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
9 Worked Out Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
9.1 Worked Out Example 1 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . 6
9.2 Worked Out Example 2 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . 6
9.3 Worked Out Example 3 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . 7
9.4 Worked Out Example 4 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . 7
9.5 Worked Out Example 5 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . 7
9.6 Worked Out Example 6 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . 7
9.7 Worked Out Example 7 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . 7
9.8 Worked Out Example 8 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . 8
9.9 Worked Out Example 9 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . 8
9.10 Worked Out Example 10 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . 8
1
1 Introduction
Newton’s laws of motion are super important in physics because they tell us how
things move when pushed or pulled. These laws help us ?gure out the motion of
objectslikeballs, cars, orevenplanets. Buttousethem, weneedtounderstandafew
basics: mass (how much stuff an object has), force (a push or pull), and acceleration
(how quickly an object’s speed or direction changes). These ideas are connected to
Newton’s laws, and sometimes the laws help de?ne them. For now, we’ll assume
youknowhowtomeasuremass, force, andacceleration, andwe’llfocusonusingthe
laws in a simple way to solve problems.
2 First Law of Motion
Newton’s First Law says: If no net force acts on an object, it either stays still or keeps
moving in a straight line at a constant speed. In other words, if the total force (net
force) on an object is zero, it has no acceleration. Mathematically:
? a =
?
0 if and only if
?
F =
?
0
This means if the forces balance out, the object doesn’t speed up, slow down, or
change direction. For example, a book on a table doesn’t move because the table’s
upward push cancels out gravity’s downward pull. If a car moves at a steady speed,
the net force is zero too.
But, whether an object is “still” or “moving” depends on your viewpoint, called the
frame of reference. Imagine a lamp hanging in an elevator that’s falling freely. To
someone inside the elevator, the lamp looks still, but to someone on the ground, it’s
fallingfast. Newton’s?rstlawonlyworksinspecialviewpointscalledinertialframes,
where objects behave as expected (no net force means no acceleration). Places like a
falling elevator, where this doesn’t work, are called noninertial frames.
Here’s an example: Imagine a lamp hanging from a rope in an elevator that falls
when the rope breaks. From inside, the lamp seems still, so net force = 0. From the
ground, it’s falling at 9.8 m/sš, so the net force seems nonzero. This shows the ?rst
lawdoesn’tworkintheelevatorframe(noninertial).
Page 3


Newton’s Laws of Motion
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 First Law of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.1 Example 5.1 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.2 Inertial Frames Other Than Earth . . . . . . . . . . . . . . . . . . . . . . . 3
3 Second Law of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
3.1 Example 5.2 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
4 Working with Newton’s First and Second Laws . . . . . . . . . . . . . . . . . 3
4.1 Example 5.3 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
5 Third Law of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
5.1 Example 5.4 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
5.2 Working with Tension in a String . . . . . . . . . . . . . . . . . . . . . . . 5
5.3 Example 5.5 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
6 Pseudo Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
7 The Horse and the Cart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
8 Inertia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
9 Worked Out Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
9.1 Worked Out Example 1 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . 6
9.2 Worked Out Example 2 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . 6
9.3 Worked Out Example 3 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . 7
9.4 Worked Out Example 4 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . 7
9.5 Worked Out Example 5 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . 7
9.6 Worked Out Example 6 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . 7
9.7 Worked Out Example 7 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . 7
9.8 Worked Out Example 8 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . 8
9.9 Worked Out Example 9 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . 8
9.10 Worked Out Example 10 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . 8
1
1 Introduction
Newton’s laws of motion are super important in physics because they tell us how
things move when pushed or pulled. These laws help us ?gure out the motion of
objectslikeballs, cars, orevenplanets. Buttousethem, weneedtounderstandafew
basics: mass (how much stuff an object has), force (a push or pull), and acceleration
(how quickly an object’s speed or direction changes). These ideas are connected to
Newton’s laws, and sometimes the laws help de?ne them. For now, we’ll assume
youknowhowtomeasuremass, force, andacceleration, andwe’llfocusonusingthe
laws in a simple way to solve problems.
2 First Law of Motion
Newton’s First Law says: If no net force acts on an object, it either stays still or keeps
moving in a straight line at a constant speed. In other words, if the total force (net
force) on an object is zero, it has no acceleration. Mathematically:
? a =
?
0 if and only if
?
F =
?
0
This means if the forces balance out, the object doesn’t speed up, slow down, or
change direction. For example, a book on a table doesn’t move because the table’s
upward push cancels out gravity’s downward pull. If a car moves at a steady speed,
the net force is zero too.
But, whether an object is “still” or “moving” depends on your viewpoint, called the
frame of reference. Imagine a lamp hanging in an elevator that’s falling freely. To
someone inside the elevator, the lamp looks still, but to someone on the ground, it’s
fallingfast. Newton’s?rstlawonlyworksinspecialviewpointscalledinertialframes,
where objects behave as expected (no net force means no acceleration). Places like a
falling elevator, where this doesn’t work, are called noninertial frames.
Here’s an example: Imagine a lamp hanging from a rope in an elevator that falls
when the rope breaks. From inside, the lamp seems still, so net force = 0. From the
ground, it’s falling at 9.8 m/sš, so the net force seems nonzero. This shows the ?rst
lawdoesn’tworkintheelevatorframe(noninertial).
Page 4


Newton’s Laws of Motion
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 First Law of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.1 Example 5.1 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.2 Inertial Frames Other Than Earth . . . . . . . . . . . . . . . . . . . . . . . 3
3 Second Law of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
3.1 Example 5.2 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
4 Working with Newton’s First and Second Laws . . . . . . . . . . . . . . . . . 3
4.1 Example 5.3 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
5 Third Law of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
5.1 Example 5.4 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
5.2 Working with Tension in a String . . . . . . . . . . . . . . . . . . . . . . . 5
5.3 Example 5.5 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
6 Pseudo Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
7 The Horse and the Cart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
8 Inertia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
9 Worked Out Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
9.1 Worked Out Example 1 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . 6
9.2 Worked Out Example 2 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . 6
9.3 Worked Out Example 3 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . 7
9.4 Worked Out Example 4 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . 7
9.5 Worked Out Example 5 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . 7
9.6 Worked Out Example 6 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . 7
9.7 Worked Out Example 7 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . 7
9.8 Worked Out Example 8 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . 8
9.9 Worked Out Example 9 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . 8
9.10 Worked Out Example 10 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . 8
1
1 Introduction
Newton’s laws of motion are super important in physics because they tell us how
things move when pushed or pulled. These laws help us ?gure out the motion of
objectslikeballs, cars, orevenplanets. Buttousethem, weneedtounderstandafew
basics: mass (how much stuff an object has), force (a push or pull), and acceleration
(how quickly an object’s speed or direction changes). These ideas are connected to
Newton’s laws, and sometimes the laws help de?ne them. For now, we’ll assume
youknowhowtomeasuremass, force, andacceleration, andwe’llfocusonusingthe
laws in a simple way to solve problems.
2 First Law of Motion
Newton’s First Law says: If no net force acts on an object, it either stays still or keeps
moving in a straight line at a constant speed. In other words, if the total force (net
force) on an object is zero, it has no acceleration. Mathematically:
? a =
?
0 if and only if
?
F =
?
0
This means if the forces balance out, the object doesn’t speed up, slow down, or
change direction. For example, a book on a table doesn’t move because the table’s
upward push cancels out gravity’s downward pull. If a car moves at a steady speed,
the net force is zero too.
But, whether an object is “still” or “moving” depends on your viewpoint, called the
frame of reference. Imagine a lamp hanging in an elevator that’s falling freely. To
someone inside the elevator, the lamp looks still, but to someone on the ground, it’s
fallingfast. Newton’s?rstlawonlyworksinspecialviewpointscalledinertialframes,
where objects behave as expected (no net force means no acceleration). Places like a
falling elevator, where this doesn’t work, are called noninertial frames.
Here’s an example: Imagine a lamp hanging from a rope in an elevator that falls
when the rope breaks. From inside, the lamp seems still, so net force = 0. From the
ground, it’s falling at 9.8 m/sš, so the net force seems nonzero. This shows the ?rst
lawdoesn’tworkintheelevatorframe(noninertial).
• The string pulls up with tension T.
The particle is still (no acceleration), so the net force is zero. Thus, T-5.88 = 0, so
T = 5.88N upward.
2.2 Inertial Frames Other Than Earth
Ifaframemovesataconstantspeedrelativetoaninertialframe,it’salsoinertial. For
example, if frame S is inertial (like Earth), and frame S’ (like a train) moves steadily
relative to S, the acceleration of an object is the same in both frames. So, S’ is inertial
too. Examples include a plane ?ying steadily or a ship sailing smoothly. In these
frames, Newton’s ?rst law holds: no net force means no acceleration.
3 Second Law of Motion
Newton’s Second Law says: The acceleration of an object in an inertial frame equals
the net force on it divided by its mass. Mathematically:
?
F = m? a or ? a =
?
F
m
This means the net force (
?
F, the total of all forces) causes an object to accelerate, and
the acceleration depends on the object’s mass (m). For example, pushing a 10 kg box
with 20 N makes it accelerate at 20/10 = 2m/s
2
. If the force stops, the acceleration
stopsinstantly. Thislawonlyworksininertialframesandisakeyruleofhownature
works.
3.1 Example 5.2 (Modi?ed)
A6kgblockonasmoothhorizontaltableispulledbyastringat 25? rtothehorizontal,
with an acceleration of 1.5 m/sš. Find the string’s force and the table’s force on the
block. Use g = 10m/s
2
.
Solution: System: block. Forces:
• Gravity: 6×10= 60N downward.
• Normal force by table: N upward.
• Tension by string: T at 25? r.
X-axis (right, along acceleration): Tcos25
?
= 6×1.5, T×0.906 = 9, T ˜ 9.93N. Y-
axis(up,noacceleration): N+Tsin25
?
-60= 0, N+9.93×0.423= 60, N ˜ 55.80N.
4 Working with Newton’s First and Second Laws
Newton’s laws apply to a single object or a group of objects moving together (a
system). To solve problems, all parts of the system must have the same acceleration.
Here’saclearmethodtoapplythelaws:
Page 5


Newton’s Laws of Motion
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 First Law of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.1 Example 5.1 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.2 Inertial Frames Other Than Earth . . . . . . . . . . . . . . . . . . . . . . . 3
3 Second Law of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
3.1 Example 5.2 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
4 Working with Newton’s First and Second Laws . . . . . . . . . . . . . . . . . 3
4.1 Example 5.3 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
5 Third Law of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
5.1 Example 5.4 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
5.2 Working with Tension in a String . . . . . . . . . . . . . . . . . . . . . . . 5
5.3 Example 5.5 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
6 Pseudo Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
7 The Horse and the Cart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
8 Inertia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
9 Worked Out Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
9.1 Worked Out Example 1 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . 6
9.2 Worked Out Example 2 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . 6
9.3 Worked Out Example 3 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . 7
9.4 Worked Out Example 4 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . 7
9.5 Worked Out Example 5 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . 7
9.6 Worked Out Example 6 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . 7
9.7 Worked Out Example 7 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . 7
9.8 Worked Out Example 8 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . 8
9.9 Worked Out Example 9 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . . 8
9.10 Worked Out Example 10 (Modi?ed) . . . . . . . . . . . . . . . . . . . . . 8
1
1 Introduction
Newton’s laws of motion are super important in physics because they tell us how
things move when pushed or pulled. These laws help us ?gure out the motion of
objectslikeballs, cars, orevenplanets. Buttousethem, weneedtounderstandafew
basics: mass (how much stuff an object has), force (a push or pull), and acceleration
(how quickly an object’s speed or direction changes). These ideas are connected to
Newton’s laws, and sometimes the laws help de?ne them. For now, we’ll assume
youknowhowtomeasuremass, force, andacceleration, andwe’llfocusonusingthe
laws in a simple way to solve problems.
2 First Law of Motion
Newton’s First Law says: If no net force acts on an object, it either stays still or keeps
moving in a straight line at a constant speed. In other words, if the total force (net
force) on an object is zero, it has no acceleration. Mathematically:
? a =
?
0 if and only if
?
F =
?
0
This means if the forces balance out, the object doesn’t speed up, slow down, or
change direction. For example, a book on a table doesn’t move because the table’s
upward push cancels out gravity’s downward pull. If a car moves at a steady speed,
the net force is zero too.
But, whether an object is “still” or “moving” depends on your viewpoint, called the
frame of reference. Imagine a lamp hanging in an elevator that’s falling freely. To
someone inside the elevator, the lamp looks still, but to someone on the ground, it’s
fallingfast. Newton’s?rstlawonlyworksinspecialviewpointscalledinertialframes,
where objects behave as expected (no net force means no acceleration). Places like a
falling elevator, where this doesn’t work, are called noninertial frames.
Here’s an example: Imagine a lamp hanging from a rope in an elevator that falls
when the rope breaks. From inside, the lamp seems still, so net force = 0. From the
ground, it’s falling at 9.8 m/sš, so the net force seems nonzero. This shows the ?rst
lawdoesn’tworkintheelevatorframe(noninertial).
• The string pulls up with tension T.
The particle is still (no acceleration), so the net force is zero. Thus, T-5.88 = 0, so
T = 5.88N upward.
2.2 Inertial Frames Other Than Earth
Ifaframemovesataconstantspeedrelativetoaninertialframe,it’salsoinertial. For
example, if frame S is inertial (like Earth), and frame S’ (like a train) moves steadily
relative to S, the acceleration of an object is the same in both frames. So, S’ is inertial
too. Examples include a plane ?ying steadily or a ship sailing smoothly. In these
frames, Newton’s ?rst law holds: no net force means no acceleration.
3 Second Law of Motion
Newton’s Second Law says: The acceleration of an object in an inertial frame equals
the net force on it divided by its mass. Mathematically:
?
F = m? a or ? a =
?
F
m
This means the net force (
?
F, the total of all forces) causes an object to accelerate, and
the acceleration depends on the object’s mass (m). For example, pushing a 10 kg box
with 20 N makes it accelerate at 20/10 = 2m/s
2
. If the force stops, the acceleration
stopsinstantly. Thislawonlyworksininertialframesandisakeyruleofhownature
works.
3.1 Example 5.2 (Modi?ed)
A6kgblockonasmoothhorizontaltableispulledbyastringat 25? rtothehorizontal,
with an acceleration of 1.5 m/sš. Find the string’s force and the table’s force on the
block. Use g = 10m/s
2
.
Solution: System: block. Forces:
• Gravity: 6×10= 60N downward.
• Normal force by table: N upward.
• Tension by string: T at 25? r.
X-axis (right, along acceleration): Tcos25
?
= 6×1.5, T×0.906 = 9, T ˜ 9.93N. Y-
axis(up,noacceleration): N+Tsin25
?
-60= 0, N+9.93×0.423= 60, N ˜ 55.80N.
4 Working with Newton’s First and Second Laws
Newton’s laws apply to a single object or a group of objects moving together (a
system). To solve problems, all parts of the system must have the same acceleration.
Here’saclearmethodtoapplythelaws:
1. Choose the System: Pick the object(s) to study, like a block or two blocks tied
together. All parts must accelerate the same way. For example, two blocks
connectedbyastringandmovingtogethercanbeonesystem.
2. Identify Forces: List forces acting on the system from outside objects (e.g.,
gravity, tension, normal force). Don’t include forces the system applies to oth-
ers. For a block on a table, list gravity (down) and normal force (up), not the
block’sforceonthetable.
3. Draw a Free Body Diagram (FBD): Imagine the system as a dot and draw
arrows for each force, showing their directions. For a block pulled by a string,
drawarrowsforgravity(down),normalforce(up),andtension(alongstring).

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FAQs on HC Verma Summary: Newton`s Laws of Motion - Physics Class 11 - NEET

1. What are Newton's three laws of motion?

Ans.Newton's three laws of motion are fundamental principles that describe the relationship between the motion of an object and the forces acting upon it. The first law, also known as the law of inertia, states that an object at rest will remain at rest, and an object in motion will remain in motion at a constant velocity unless acted upon by a net external force. The second law defines the relationship between force, mass, and acceleration, stating that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass (F=ma). The third law states that for every action, there is an equal and opposite reaction.

2. How can Newton's laws of motion be applied in real-life scenarios?

Ans.Newton's laws of motion can be observed in various real-life scenarios. For example, when driving a car, the first law explains why passengers lurch forward when the car suddenly stops; their bodies want to continue moving due to inertia. The second law can be seen when a heavier object requires more force to accelerate than a lighter one—like pushing a shopping cart. Finally, the third law is exemplified when a swimmer pushes water backward to propel themselves forward; the action of pushing water results in the reaction that moves the swimmer.

3. What is the significance of the concept of inertia in Newton's first law?

Ans.The concept of inertia is crucial in understanding Newton's first law of motion, as it defines the tendency of an object to resist changes in its state of motion. Inertia explains why objects remain at rest or continue moving uniformly unless a net external force causes a change. This concept helps us understand not only the behavior of objects in motion but also the importance of forces in altering that motion, thereby providing a foundation for the study of dynamics in physics.

4. How does the second law of motion relate to everyday activities?

Ans.The second law of motion relates to everyday activities by illustrating how force, mass, and acceleration interact. For instance, when lifting a heavy box, you must exert a greater force compared to lifting a lighter one to achieve the same acceleration. This law also explains why athletes can accelerate quickly; they apply a larger force relative to their body mass, resulting in greater acceleration. Additionally, it explains why vehicles require more power to accelerate when carrying heavier loads.

5. What are common misconceptions about Newton's laws of motion?

Ans.Common misconceptions about Newton's laws include the misunderstanding that a force is required to keep an object in motion. In reality, according to the first law, an object will continue to move at a constant velocity unless acted upon by a net external force. Another misconception is that action and reaction forces cancel each other out; however, they act on different objects and do not cancel each other in a single system, which is key to understanding motion and forces.

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