Important Formulas: Laws of Motion | Physics Class 11 - NEET PDF Download

 Page 1


 
1. From third law of motion
BA AB F F ? ?
AB F
 = Force on A due to B
BA F
 = Force on B due to A A
2. From second law of motion
F
x
 = 
dt
dP
x
 = ma
x
F
y
 = 
dt
dP
y
 = ma
y
F
z
 = 
dt
dP
z
 = ma
z
5. WEIGHING MACHINE :
A weighing machine does not measure the weight but measures the
force exerted by object on its upper surface.
6. SPRING FORCE
x k F
?
?
? ?
x is displacement of the free end from its natural length or deformation
of the spring where K = spring constant.
7. SPRING PROPERTY K × ? = constant
= Natural length of spring.
8. If spring is cut into two in the ratio m : n then spring constant is given
by
?
1
 = 
n m
m
?
?
; ?
2
 = 
n m
. n
?
?
     k ? = k
1
?
1
 = k
2
?
2
Page 2


 
1. From third law of motion
BA AB F F ? ?
AB F
 = Force on A due to B
BA F
 = Force on B due to A A
2. From second law of motion
F
x
 = 
dt
dP
x
 = ma
x
F
y
 = 
dt
dP
y
 = ma
y
F
z
 = 
dt
dP
z
 = ma
z
5. WEIGHING MACHINE :
A weighing machine does not measure the weight but measures the
force exerted by object on its upper surface.
6. SPRING FORCE
x k F
?
?
? ?
x is displacement of the free end from its natural length or deformation
of the spring where K = spring constant.
7. SPRING PROPERTY K × ? = constant
= Natural length of spring.
8. If spring is cut into two in the ratio m : n then spring constant is given
by
?
1
 = 
n m
m
?
?
; ?
2
 = 
n m
. n
?
?
     k ? = k
1
?
1
 = k
2
?
2
For series combination of springs     
.......
k
1
k
1
k
1
2 1 eq
? ? ?
For parallel combination of spring      k
eq
 = k
1
 + k
2
 + k
3
 ............
9. SPRING BALANCE:
It does not measure the weight. ?t measures the force exerted by the
object at the hook.
Remember :
V
p
 = 
1 2
V V
2
?
a
P
 = 
1 2
a a
2
?
11.
2 1
1 2
m m
g ) m m (
a
?
?
?
2 1
2 1
m m
g m m 2
T
?
?
12. WEDGE CONSTRAINT:
Components of velocity along perpendicular direction to the contact
plane of the two objects is always equal if there is no deformations
and they remain in contact.
Page 3


 
1. From third law of motion
BA AB F F ? ?
AB F
 = Force on A due to B
BA F
 = Force on B due to A A
2. From second law of motion
F
x
 = 
dt
dP
x
 = ma
x
F
y
 = 
dt
dP
y
 = ma
y
F
z
 = 
dt
dP
z
 = ma
z
5. WEIGHING MACHINE :
A weighing machine does not measure the weight but measures the
force exerted by object on its upper surface.
6. SPRING FORCE
x k F
?
?
? ?
x is displacement of the free end from its natural length or deformation
of the spring where K = spring constant.
7. SPRING PROPERTY K × ? = constant
= Natural length of spring.
8. If spring is cut into two in the ratio m : n then spring constant is given
by
?
1
 = 
n m
m
?
?
; ?
2
 = 
n m
. n
?
?
     k ? = k
1
?
1
 = k
2
?
2
For series combination of springs     
.......
k
1
k
1
k
1
2 1 eq
? ? ?
For parallel combination of spring      k
eq
 = k
1
 + k
2
 + k
3
 ............
9. SPRING BALANCE:
It does not measure the weight. ?t measures the force exerted by the
object at the hook.
Remember :
V
p
 = 
1 2
V V
2
?
a
P
 = 
1 2
a a
2
?
11.
2 1
1 2
m m
g ) m m (
a
?
?
?
2 1
2 1
m m
g m m 2
T
?
?
12. WEDGE CONSTRAINT:
Components of velocity along perpendicular direction to the contact
plane of the two objects is always equal if there is no deformations
and they remain in contact.
13. NEWTON’S LAW FOR A SYSTEM
ext 1 1 2 2 3 3
F m a m a m a ...... ? ? ? ?
?
? ? ?
ext
F ?
?
Net external force on the system.
m
1
, m
2
, m
3
 are the masses of the objects of the system and
1 2 3
a ,a ,a
? ? ?
are the acceleration of the objects respectively. .
14. NEWTON’S LAW FOR NON INERTIAL FRAME :
a m F F
Pseudo al Re
?
? ?
? ?
Net sum of real and pseudo force is taken in the resultant force.
a
?
 = Acceleration of the particle in the non inertial frame
Pseudo
F
?
 = ? m 
Frame
a
?
(a) Inertial reference frame: Frame of reference moving with con-
stant velocity.
(b) Non-inertial reference frame: A frame of reference moving with
non-zero acceleration.
FRICTION
Friction force is of two types.
(a) Kinetic (b) Static
KINETIC FRICTION : f
k
 = ?
k
 N
The proportionality constant ?
k
 is called the coefficient of kinetic friction
and its value depends on the nature of the two surfaces in contact.
STATIC FRICTION :
It exists between the two surfaces when there is tendency of relative mo-
tion but no relative motion along the two contact surfaces.
This means static friction is a variable and self adjusting force.
However it has a maximum value called limiting friction.
f
max 
= ?
s
N
0 
?
 f
s
 
?
 f
smax
Friction 
Applied Force
static friction
f 
static maximum
?
s
N ?
k
N
Page 4


 
1. From third law of motion
BA AB F F ? ?
AB F
 = Force on A due to B
BA F
 = Force on B due to A A
2. From second law of motion
F
x
 = 
dt
dP
x
 = ma
x
F
y
 = 
dt
dP
y
 = ma
y
F
z
 = 
dt
dP
z
 = ma
z
5. WEIGHING MACHINE :
A weighing machine does not measure the weight but measures the
force exerted by object on its upper surface.
6. SPRING FORCE
x k F
?
?
? ?
x is displacement of the free end from its natural length or deformation
of the spring where K = spring constant.
7. SPRING PROPERTY K × ? = constant
= Natural length of spring.
8. If spring is cut into two in the ratio m : n then spring constant is given
by
?
1
 = 
n m
m
?
?
; ?
2
 = 
n m
. n
?
?
     k ? = k
1
?
1
 = k
2
?
2
For series combination of springs     
.......
k
1
k
1
k
1
2 1 eq
? ? ?
For parallel combination of spring      k
eq
 = k
1
 + k
2
 + k
3
 ............
9. SPRING BALANCE:
It does not measure the weight. ?t measures the force exerted by the
object at the hook.
Remember :
V
p
 = 
1 2
V V
2
?
a
P
 = 
1 2
a a
2
?
11.
2 1
1 2
m m
g ) m m (
a
?
?
?
2 1
2 1
m m
g m m 2
T
?
?
12. WEDGE CONSTRAINT:
Components of velocity along perpendicular direction to the contact
plane of the two objects is always equal if there is no deformations
and they remain in contact.
13. NEWTON’S LAW FOR A SYSTEM
ext 1 1 2 2 3 3
F m a m a m a ...... ? ? ? ?
?
? ? ?
ext
F ?
?
Net external force on the system.
m
1
, m
2
, m
3
 are the masses of the objects of the system and
1 2 3
a ,a ,a
? ? ?
are the acceleration of the objects respectively. .
14. NEWTON’S LAW FOR NON INERTIAL FRAME :
a m F F
Pseudo al Re
?
? ?
? ?
Net sum of real and pseudo force is taken in the resultant force.
a
?
 = Acceleration of the particle in the non inertial frame
Pseudo
F
?
 = ? m 
Frame
a
?
(a) Inertial reference frame: Frame of reference moving with con-
stant velocity.
(b) Non-inertial reference frame: A frame of reference moving with
non-zero acceleration.
FRICTION
Friction force is of two types.
(a) Kinetic (b) Static
KINETIC FRICTION : f
k
 = ?
k
 N
The proportionality constant ?
k
 is called the coefficient of kinetic friction
and its value depends on the nature of the two surfaces in contact.
STATIC FRICTION :
It exists between the two surfaces when there is tendency of relative mo-
tion but no relative motion along the two contact surfaces.
This means static friction is a variable and self adjusting force.
However it has a maximum value called limiting friction.
f
max 
= ?
s
N
0 
?
 f
s
 
?
 f
smax
Friction 
Applied Force
static friction
f 
static maximum
?
s
N ?
k
N
1. Average angular velocity ? ?
av
 = 
1 2
1 2
t t ?
? ? ?
 = 
t ?
? ?
2. Instantaneous angular velocity ? ? = 
dt
d ?
?
?
3. Average angular acceleration ? ?
av
 = 
1 2
1 2
t t ?
? ? ?
 = 
t
? ?
?
4. Instantaneous angular acceleration ? ? = 
dt
d ?
 = ?
?
?
d
d
5. Relation between speed and angular velocity   ? v = r ? and 
r v
? ? ?
? ? ?
7. Tangential acceleration (rate of change of speed)
? a
t
 = 
dt
dV
 = r 
dt
d ?
 =  ? 
dt
dr
8. Radial or normal or centripetal acceleration ? ? ? ? a
r
 = 
r
v
2
= ?
2
r
9. Total acceleration
?
r t
a a a
? ? ?
? ? ? a = (a
t
2
 + a
r
2
)
1/2
   
r
a
c
a
a
t
a
v
or
?
P
O
Where r a
t
? ? ?
? ? ? and v a
r
? ? ?
? ? ?
Page 5


 
1. From third law of motion
BA AB F F ? ?
AB F
 = Force on A due to B
BA F
 = Force on B due to A A
2. From second law of motion
F
x
 = 
dt
dP
x
 = ma
x
F
y
 = 
dt
dP
y
 = ma
y
F
z
 = 
dt
dP
z
 = ma
z
5. WEIGHING MACHINE :
A weighing machine does not measure the weight but measures the
force exerted by object on its upper surface.
6. SPRING FORCE
x k F
?
?
? ?
x is displacement of the free end from its natural length or deformation
of the spring where K = spring constant.
7. SPRING PROPERTY K × ? = constant
= Natural length of spring.
8. If spring is cut into two in the ratio m : n then spring constant is given
by
?
1
 = 
n m
m
?
?
; ?
2
 = 
n m
. n
?
?
     k ? = k
1
?
1
 = k
2
?
2
For series combination of springs     
.......
k
1
k
1
k
1
2 1 eq
? ? ?
For parallel combination of spring      k
eq
 = k
1
 + k
2
 + k
3
 ............
9. SPRING BALANCE:
It does not measure the weight. ?t measures the force exerted by the
object at the hook.
Remember :
V
p
 = 
1 2
V V
2
?
a
P
 = 
1 2
a a
2
?
11.
2 1
1 2
m m
g ) m m (
a
?
?
?
2 1
2 1
m m
g m m 2
T
?
?
12. WEDGE CONSTRAINT:
Components of velocity along perpendicular direction to the contact
plane of the two objects is always equal if there is no deformations
and they remain in contact.
13. NEWTON’S LAW FOR A SYSTEM
ext 1 1 2 2 3 3
F m a m a m a ...... ? ? ? ?
?
? ? ?
ext
F ?
?
Net external force on the system.
m
1
, m
2
, m
3
 are the masses of the objects of the system and
1 2 3
a ,a ,a
? ? ?
are the acceleration of the objects respectively. .
14. NEWTON’S LAW FOR NON INERTIAL FRAME :
a m F F
Pseudo al Re
?
? ?
? ?
Net sum of real and pseudo force is taken in the resultant force.
a
?
 = Acceleration of the particle in the non inertial frame
Pseudo
F
?
 = ? m 
Frame
a
?
(a) Inertial reference frame: Frame of reference moving with con-
stant velocity.
(b) Non-inertial reference frame: A frame of reference moving with
non-zero acceleration.
FRICTION
Friction force is of two types.
(a) Kinetic (b) Static
KINETIC FRICTION : f
k
 = ?
k
 N
The proportionality constant ?
k
 is called the coefficient of kinetic friction
and its value depends on the nature of the two surfaces in contact.
STATIC FRICTION :
It exists between the two surfaces when there is tendency of relative mo-
tion but no relative motion along the two contact surfaces.
This means static friction is a variable and self adjusting force.
However it has a maximum value called limiting friction.
f
max 
= ?
s
N
0 
?
 f
s
 
?
 f
smax
Friction 
Applied Force
static friction
f 
static maximum
?
s
N ?
k
N
1. Average angular velocity ? ?
av
 = 
1 2
1 2
t t ?
? ? ?
 = 
t ?
? ?
2. Instantaneous angular velocity ? ? = 
dt
d ?
?
?
3. Average angular acceleration ? ?
av
 = 
1 2
1 2
t t ?
? ? ?
 = 
t
? ?
?
4. Instantaneous angular acceleration ? ? = 
dt
d ?
 = ?
?
?
d
d
5. Relation between speed and angular velocity   ? v = r ? and 
r v
? ? ?
? ? ?
7. Tangential acceleration (rate of change of speed)
? a
t
 = 
dt
dV
 = r 
dt
d ?
 =  ? 
dt
dr
8. Radial or normal or centripetal acceleration ? ? ? ? a
r
 = 
r
v
2
= ?
2
r
9. Total acceleration
?
r t
a a a
? ? ?
? ? ? a = (a
t
2
 + a
r
2
)
1/2
   
r
a
c
a
a
t
a
v
or
?
P
O
Where r a
t
? ? ?
? ? ? and v a
r
? ? ?
? ? ?
10. Angular acceleration
?
?
?
 = 
dt
d ?
?
 (Non-uniform circular motion) 
?
ACW
Rotation
12. Radius of curvature R = 
?
a
v
2
 = 
?
F
mv
2
If y is a function of x.      i.e. y = f(x) ? R = 
2
2
2 / 3
2
dx
y d
dx
dy
1
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
13. Normal reaction of road on a concave bridge
? N = mg cos ? + 
r
mv
2
?
?
N
V
mg
mgcos ?
concave 
bridge
O
14. Normal reaction on a convex bridge
? N = mg cos ? – 
r
mv
2
?
N
V
mg
mgcos ?
convex 
bridge
O
?
15. Skidding of vehicle on a level road ? v
safe
 ? gr ?
16. Skidding of an object on a rotating platform ? ?
max
 = r / g ?