What this chapter is about
This chapter connects the ideas of force and motion that you began studying earlier. You already know that objects move, speed up, slow down or change direction. Now you will learn exactly how forces cause these changes. The chapter introduces Newton's three laws of motion, which explain why a book stays still on a table, why you lurch forward when a bus brakes suddenly, and why a cricket ball hurts your hand when you catch it.
You will also learn about momentum, a quantity that combines mass and velocity. Understanding momentum helps explain collisions, rocket propulsion and many everyday events. By the end of this chapter you should be able to state each law, use it to predict what happens in a given situation, and solve numerical problems involving force, mass, acceleration and momentum.
This topic matters because almost every branch of science and engineering uses Newton's laws. Whether you later study machines, vehicles, sports science or space travel, you will rely on these ideas again and again.
Key ideas
- A force is a push or pull that can change an object's state of rest or of uniform motion in a straight line.
- Newton's first law (law of inertia): An object remains at rest or continues moving with constant velocity unless acted upon by an unbalanced external force.
- Inertia is the tendency of an object to resist any change in its motion; it depends only on mass.
- Newton's second law: The net force on an object equals the product of its mass and its acceleration (F = m × a). Force is measured in newtons (N), where 1 N = 1 kg × 1 m/s².
- Newton's third law: When object A exerts a force on object B, object B exerts an equal and opposite force on object A; these two forces act on different bodies.
- Momentum (p) equals mass times velocity (p = m × v); its SI unit is kg m/s.
- The law of conservation of momentum states that the total momentum of an isolated system remains constant before and after a collision or explosion.
Formulas and facts to remember
- Force: F = m × a (force equals mass multiplied by acceleration)
- Momentum: p = m × v (momentum equals mass multiplied by velocity)
- Change in momentum: Δp = F × t (impulse equals force multiplied by time)
- Newton's second law in momentum form: F = (m × v − m × u) / t, where u is initial velocity and v is final velocity
- 1 newton is the force needed to give a 1 kg mass an acceleration of 1 m/s²
- In the absence of external forces, total momentum before interaction = total momentum after interaction
- Action and reaction forces are always equal in magnitude, opposite in direction, and act on two different objects
Worked examples
Example 1: Calculating force
A scooter of mass 80 kg accelerates uniformly from rest to 10 m/s in 5 s. Find the net force acting on it.
Step 1: Find acceleration. a = (v − u) / t = (10 − 0) / 5 = 2 m/s²
Step 2: Apply Newton's second law. F = m × a = 80 × 2 = 160 N
The net force on the scooter is 160 N in the direction of motion.
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Example 2: Momentum and impulse
A cricket ball of mass 0.15 kg moving at 20 m/s is stopped by a fielder in 0.1 s. What average force does the fielder apply?
Step 1: Find change in momentum. Δp = m × (v − u) = 0.15 × (0 − 20) = −3 kg m/s
Step 2: Calculate force. F = Δp / t = −3 / 0.1 = −30 N
The magnitude of the average force is 30 N. The negative sign shows the force opposes the ball's original motion.
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Example 3: Conservation of momentum
A 50 kg girl standing on a stationary 10 kg skateboard jumps forward with a velocity of 2 m/s relative to the ground. What is the velocity of the skateboard immediately after she jumps?
Step 1: Total initial momentum is zero (both at rest). p_initial = 0
Step 2: After the jump, momentum is conserved. m_girl × v_girl + m_board × v_board = 0 50 × 2 + 10 × v_board = 0 100 + 10 × v_board = 0 v_board = −10 m/s
The skateboard moves backward at 10 m/s.
Common mistakes
- Thinking a moving object needs a constant force to keep moving → An object in motion continues at constant velocity without any force; force is needed only to change velocity.
- Applying action and reaction to the same body → Action and reaction act on two different objects, so they do not cancel each other.
- Forgetting that velocity and momentum are vector quantities → Always note direction; a change in direction means a change in velocity even if speed stays the same.
- Using weight instead of mass in F = m × a → Mass (kg) goes into the formula; weight is the gravitational force (N) on that mass.
- Ignoring units and mixing grams with kilograms → Convert grams to kilograms before substituting into SI formulas.
Quick revision
- First law: No unbalanced force means no change in motion.
- Second law: F = m × a links force, mass and acceleration.
- Third law: Every action has an equal and opposite reaction on another body.
- Momentum = mass × velocity; its unit is kg m/s.
- Total momentum of an isolated system stays constant.
- Inertia depends on mass: heavier objects are harder to accelerate or stop.