Laws of Motion: common doubts, answered
The questions students ask most often about Laws of Motion, each with a short answer. For the full chapter, read the Laws of Motion notes.
Aristotle's fallacy and the law of inertia
Read this section in the notes →Does a moving body need a force to keep moving?
No. A body keeps moving at constant velocity unless a net external force acts on it. In everyday life we must keep pushing only because friction and air drag oppose the motion; the applied force just cancels them. Remove those opposing forces and the body would carry on forever, which is what Galileo concluded from his inclined-plane reasoning.
Newton's first law of motion
Read this section in the notes →Why does a passenger fall forward when a bus brakes suddenly?
Because of inertia: the passenger's body tends to keep moving forward at the bus's earlier speed. The brakes slow the bus and, through friction, the passenger's feet, but the upper body is not held and continues forward for a moment. In the same way a passenger falls backward when a bus starts suddenly from rest.
What is the difference between mass and inertia?
Inertia is the property of resisting a change in motion, and mass is the quantitative measure of that property. A body with greater mass is harder to start, stop or turn. Mass is a number in kilograms, while inertia is the name for the behaviour itself, so the two are closely linked rather than identical words for one idea.
Newton's second law, momentum and impulse
Read this section in the notes →Why is Newton's second law written as F = dp/dt instead of F = ma?
Because F = dp/dt is the more general form: it states that force equals the rate of change of momentum. When the mass is constant, it reduces to F = ma. Writing it in terms of momentum also leads directly to the idea of impulse and makes clear why stopping a fast or heavy object needs a large force or a long time.
Why does a cricketer pull the hands back while catching a ball?
Pulling the hands back increases the time over which the ball is stopped. The change in momentum is fixed by the ball's mass and speed, and since impulse J = FΔt = Δp, a longer stopping time means a smaller average force on the hands. The same idea explains why falling on sand hurts less than falling on concrete.
How do you find the change in momentum when a ball bounces back from a wall?
Take the velocities with signs. If a ball of mass m hits a wall at speed v and rebounds at the same speed, its momentum goes from +mv to −mv, so the change is −2mv, not zero. Subtracting speeds without directions is the classic mistake; momentum is a vector and reversing direction counts as a change.
Newton's third law of motion
Read this section in the notes →If action and reaction are equal and opposite, why don't they cancel?
Because they act on different bodies. When you push a wall, your hand pushes the wall and the wall pushes your hand. Forces cancel only when they act on the same body, so an action-reaction pair can never balance each other. Whether a body accelerates depends only on the forces acting on that body.
If the Earth pulls an apple, does the apple pull the Earth?
Yes, with exactly the same force in the opposite direction. The Earth does not visibly move because its mass is enormous, so the same force gives it a negligible acceleration. Both forces exist at the same time; the third law does not mean one force is the cause and the other a later response.
Conservation of momentum
Read this section in the notes →Why does a gun recoil when fired?
Because the total momentum of gun and bullet is zero before firing and must stay zero, as long as no external horizontal force acts. The bullet gains forward momentum, so the gun gains equal momentum backwards, giving a recoil speed V = −(m/M)v. The gun's large mass keeps its recoil speed much smaller than the bullet's speed.
When is linear momentum conserved?
The total momentum of a system is conserved whenever the net external force on it is zero. Internal forces between parts of the system come in action-reaction pairs and cancel in the total. Momentum can also be conserved along one direction alone if there is no external force along that direction, even when forces act in other directions.
Equilibrium of a particle
Read this section in the notes →What does it mean for a particle to be in equilibrium?
It means the net force on the particle is zero, so it stays at rest or moves with constant velocity. In components, ΣFx = 0 and ΣFy = 0. Three forces can keep a particle in equilibrium if they form a closed triangle when drawn head to tail. Zero net force does not require the particle to be at rest.
Common forces in mechanics
Read this section in the notes →Why do you feel heavier in a lift accelerating upward?
Because the floor must push on you with more than your weight to accelerate you upward: R = m(g + a). The weighing scale reads this normal force, so it shows more than mg. What matters is the direction of acceleration, not of motion; a lift moving up but slowing down makes you feel lighter, with R = m(g − a).
Is the normal force always equal to mg?
No. It equals mg only for a body resting on a horizontal surface with no other vertical forces and no vertical acceleration. If a pulling force acts at an angle above the horizontal, its upward part reduces the normal force; pushing down at an angle increases it. On an incline the normal force is mg cos θ.
Friction
Read this section in the notes →What is the difference between static and kinetic friction?
Static friction acts when surfaces are not sliding and adjusts itself to match the applied force, up to a limit (f_s)max = μ_s N. Kinetic friction acts once sliding starts and has a roughly fixed value f_k = μ_k N. Usually μ_k is less than μ_s, which is why it is harder to start pushing a heavy box than to keep it moving.
Is static friction always equal to μ_s N?
No, μ_s N is only the maximum value. Static friction is just as large as needed to stop slipping. If you push a block with 5 N and the limit is 20 N, friction is 5 N, not 20 N. Always compare the applied force with μ_s N first: if smaller, friction equals the applied force and the block stays put.
Does friction always oppose motion?
No, friction opposes relative sliding between surfaces, not motion itself. When you walk, friction on your foot points forward and is what moves you ahead. When a box sits on an accelerating truck, friction on the box acts forward and drags it along. Friction can therefore be the force that causes motion.
Circular motion
Read this section in the notes →Is centripetal force a separate force on a free-body diagram?
No. Centripetal force is not a new kind of force; it is the name for the net inward force that some real force provides. For a car on a level curve it is friction, for a stone on a string it is tension, and for a satellite it is gravity. Draw only the real forces and set their inward sum equal to mv²/R.
Why are roads banked on curves?
Banking tilts the road so that part of the normal force points towards the centre of the curve and supplies the centripetal force. This reduces the reliance on friction and allows higher safe speeds. At the optimum speed v₀ = √(R g tan θ) no friction is needed at all, which also reduces tyre wear.
Solving problems in mechanics
Read this section in the notes →How do you solve problems with connected bodies on a string?
Draw a separate free-body diagram for each body, mark every force on it, and write Newton's second law along the direction it can move. The string links the bodies, so they share the same acceleration and the tension is the same along a light string. Solve the equations together; for two masses over a pulley, a = (m₁ − m₂)g/(m₁ + m₂).
What is a free-body diagram and why is it needed?
A free-body diagram shows one chosen body by itself with every external force acting on it drawn as an arrow. Forces the body exerts on others are left out. It is needed because Newton's second law applies to one body at a time, and the diagram makes it clear which forces enter the equation, preventing missed or double-counted forces.
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