CBSE Class 9 > Class 9 Notes > Science New NCERT 2026-27 (New Syllabus) > Cheat Sheet: How Forces Affect Motion
Cheat Sheet: How Forces Affect Motion
1. Introduction & Concept of Force
1.1 Definition & Properties
| Term | Definition |
|---|---|
| Force | Push or pull that can change motion, speed, direction, or shape |
| Vector quantity | Requires magnitude and direction |
| SI unit | Newton (symbol: N) |
| Effect dependence | Change in magnitude or direction of a force changes its effect |
1.2 Effects and Measurement
- Make an object move from rest
- Change the speed of a moving object
- Change the direction of a moving object
- Change the shape of an object
| Term | Definition |
|---|---|
| Spring balance | Instrument used to measure magnitude of a force |
| Weight | Gravitational force with which the Earth pulls an object |
| Spring balance measurement | Measures general force when the free end is pulled |
| Smallest forces felt | Order of millinewtons (10⁻³ N) |
| Smallest forces measured | Yoctonewtons (10⁻²⁴ N) in specialised experiments (as of 2026) |
2. Balanced and Unbalanced Forces
2.1 Definitions and Net Force Rules
| Term | Definition |
|---|---|
| Balanced forces | Two forces equal in magnitude and opposite in direction producing net force zero and no change in motion |
| Unbalanced forces | Forces not equal in magnitude producing a non-zero net force and causing acceleration toward the larger force |
| Opposite-direction rule | Net force = difference of magnitudes; direction of larger force |
| Same-direction rule | Net force = sum of magnitudes; direction same as both forces |
| Forces at angles | Net force requires vector addition and is more complex |
| Equal-opposite at different points | Equal and opposite forces at different points can produce rotation |
3. The Force of Friction
3.1 Definition
| Term | Definition |
|---|---|
| Friction | Force between surfaces that opposes relative motion and acts opposite to the direction of motion |
3.2 Key Facts
| Term | Definition |
|---|---|
| Dependence on surfaces | Friction depends on the nature of the contacting surfaces |
| Smoother vs rougher | Smoother surfaces have less friction; rougher surfaces have more friction |
| Effect of smaller friction | Object slows down more slowly and travels a larger distance before stopping |
| Spring balance and friction | Spring balance measures the force required to just start moving a block, equal to the force of friction |
| Friction varies | Different surfaces give different friction readings; smaller reading means less friction |
3.3 Forces on a moving object
- Applied force
- Friction
- Normal force
- Gravitational force
4. Newton's Laws of Motion
4.1 Newton's First Law
| Term | Definition |
|---|---|
| First law (statement) | An object at rest remains at rest and an object in motion continues with constant velocity unless a net force acts on it |
| Consequence | If net force is zero, acceleration is zero |
| Constant velocity | No change in magnitude or direction; non-zero constant velocity implies straight-line motion |
| Galileo | Galileo explained that no force is needed to keep an object moving at constant velocity when resistance is absent |
4.2 Graphs for Newton's First Law
- Object at rest - Position-time: horizontal straight line
- Object at rest - Velocity-time: horizontal straight line at v = 0
- Object moving with constant velocity - Position-time: straight line inclined to time axis
- Object moving with constant velocity - Velocity-time: horizontal straight line at constant non-zero value
4.3 Newton's Second Law
| Term | Definition |
|---|---|
| Second law (statement) | Net force on an object produces acceleration in direction of net force; acceleration ∝ net force and ∝ 1/mass |
| Mathematical form | a = F/m or F = ma |
| Variable meanings | a = acceleration; F = net force; m = mass |
| Definition of 1 N | One newton produces 1 m s⁻² on a mass of 1 kg (1 N = 1 kg m s⁻²) |
| Gravitational force | F = mg |
| Acceleration due to gravity | g = 9.8 m s⁻² (can be taken ≈ 10 m s⁻² for quick estimations) |
| Independence of g | Acceleration due to Earth's gravity (g) does not depend on the mass of the object |
| Force-mass relations | For fixed mass: larger force → larger acceleration; for fixed force: smaller mass → larger acceleration |
| Momentum form | Second law as rate of change of momentum proportional to net force and in its direction |
4.4 Newton's Third Law
| Term | Definition |
|---|---|
| Third law (statement) | Whenever one object exerts a force on a second, the second exerts an equal and opposite force on the first |
| Origin of forces | Forces arise due to interaction between two objects |
| Applicability | Applies to contact and non-contact forces |
| Action-reaction properties | Action and reaction have equal magnitudes, opposite directions, and act on different objects so they do not balance |
| Different accelerations | Equal forces on different masses produce different accelerations via a = F/m |
5. Forces Acting on a System of Objects
5.1 System Approach
| Term | Definition |
|---|---|
| System treatment | Treat connected objects and the string as a single system to simplify analysis |
| Internal forces | Internal forces such as tension act between parts and can be ignored for system acceleration |
| External forces | Only external forces such as applied force F determine the system acceleration |
| Acceleration of two-box system | a = F / (m₁ + m₂) for two boxes m₁ and m₂ on a frictionless surface pulled by F |
| External vertical forces | Gravitational force (m₁g + m₂g) is balanced by normal force (N₁ + N₂) |
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