Force and Laws of Motion
A force is a push or a pull that can change the state of motion of an object. This Class 9 chapter explains balanced and unbalanced forces, Newton's three laws of motion, the ideas of inertia and momentum, the relation F = ma, and the law of conservation of momentum. It connects directly to the equations of motion you learned in the previous chapter.
Learning objectives
- Distinguish balanced and unbalanced forces.
- State Newton's three laws of motion.
- Relate inertia to mass.
- Define momentum and apply F = ma.
- State and apply the law of conservation of momentum.
Key concepts
Forces and inertia
Balanced forces cancel out and cause no change in motion; unbalanced forces change an object's speed or direction. Inertia is the tendency of an object to resist a change in its state of rest or motion, and it increases with mass.
Newton's first law
An object stays at rest or in uniform motion in a straight line unless acted on by an unbalanced force. This is the law of inertia, which is why we lurch forward when a moving bus stops suddenly.
Newton's second law
The rate of change of momentum is proportional to the applied force and acts in its direction. This gives the relation F = ma, where momentum p = mv. The SI unit of force is the newton (N).
Newton's third law and conservation of momentum
For every action there is an equal and opposite reaction. In the absence of external forces, the total momentum of a system is conserved, which explains the recoil of a gun and rocket propulsion.
Important formulas
Force
F = ma
Momentum
p = mv
Newton's second law
F = (mv − mu) ÷ t = rate of change of momentum
Conservation of momentum
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
Key definitions
- Force
- A push or pull that can change the state of motion or shape of a body.
- Inertia
- The tendency of a body to resist a change in its state of rest or motion.
- Momentum
- The product of an object's mass and velocity (p = mv).
- Newton (N)
- The SI unit of force; 1 N accelerates a 1 kg mass at 1 m/s².
Solved examples
Q1. A force of 20 N acts on a mass of 4 kg. Find the acceleration.
Solution: Using F = ma: a = F/m = 20/4 = 5 m/s².
Q2. Find the momentum of a 2 kg ball moving at 3 m/s.
Solution: p = mv = 2 × 3 = 6 kg·m/s.
Q3. Why do passengers fall backward when a bus suddenly starts?
Solution: By inertia of rest, the lower body moves with the bus while the upper body tends to stay at rest, so passengers fall backward.
Common mistakes to avoid
- Thinking a moving object needs a continuous force to keep moving (it does not, without friction).
- Confusing mass (amount of matter) with inertia's cause and weight.
- Treating action and reaction as acting on the same body — they act on different bodies.
- Forgetting units: force in N, momentum in kg·m/s.
Force and Laws of Motion — MCQ Quiz
12 questions with instant feedback. Use number keys 1–4 to answer.
The tendency of a body to resist change in its motion is:
Practice questions
Short answer
State Newton's first law of motion.
A body remains at rest or in uniform motion unless acted on by an unbalanced external force.
Why are seat belts important in cars?
They prevent the body's inertia from throwing it forward during a sudden stop, reducing injury.
Define one newton.
The force that gives a 1 kg mass an acceleration of 1 m/s².
Long answer
State and explain the law of conservation of momentum with an example.
When no external force acts on a system, its total momentum stays constant. For two colliding bodies: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂. Example: when a bullet is fired, the forward momentum of the bullet equals the backward momentum of the gun, so the gun recoils — the total momentum before and after firing is zero.
Derive F = ma from Newton's second law.
Momentum p = mv. The second law says force equals the rate of change of momentum: F = (mv − mu)/t = m(v − u)/t. Since acceleration a = (v − u)/t, we get F = ma.
HOTS (Higher Order Thinking)
A karate player breaks a slab with a fast blow. Use momentum to explain why speed matters.
A very short contact time means a large rate of change of momentum, producing a large force on the slab (F = change in momentum ÷ time); the high speed of the hand maximises this force.
Why is it easier to stop a tennis ball than a cricket ball moving at the same speed?
The cricket ball has more mass and hence more momentum, so a larger force (or more time) is needed to stop it compared to the lighter tennis ball.
Quick revision
Revision notes
- Balanced forces: no change; unbalanced forces: change motion.
- First law = inertia; inertia increases with mass.
- Second law: F = ma, momentum p = mv.
- Third law: equal and opposite reactions; momentum is conserved.
Key takeaways
- Action and reaction act on different bodies.
- F = ma links force, mass and acceleration.
- Conservation of momentum explains recoil and propulsion.
Frequently asked questions
What is inertia?
The natural tendency of a body to resist any change in its state of rest or uniform motion; it increases with mass.
What is Newton's second law?
The rate of change of momentum is proportional to the applied force, giving the relation F = ma.
What does the law of conservation of momentum state?
In the absence of external forces, the total momentum of a system remains constant.