fₖ = μₖN

“A seatbelt works because your body obeys Newton's first law — it wants to keep moving when the car suddenly stops.”

Kinetic friction once the object is sliding. Use it when the object is moving.

fₖ = μₖN

mg sinθ, mg cosθ

“A seatbelt works because your body obeys Newton's first law — it wants to keep moving when the car suddenly stops.”

Weight components along and perpendicular to an incline. Use it when analysing motion on a slope.

mg sinθ, mg cosθ

static friction vs kinetic friction

“A seatbelt works because your body obeys Newton's first law — it wants to keep moving when the car suddenly stops.”

Static friction acts on a stationary object and self-adjusts up to a limit; kinetic friction acts on a sliding object and is roughly constant (and usually smaller).

mass vs weight

“A seatbelt works because your body obeys Newton's first law — it wants to keep moving when the car suddenly stops.”

Mass is the amount of matter (kg, same everywhere); weight is the gravitational force on it (N, changes with g).

inertial frame vs non-inertial frame

“A seatbelt works because your body obeys Newton's first law — it wants to keep moving when the car suddenly stops.”

An inertial frame moves at constant velocity (Newton's laws hold directly); a non-inertial frame accelerates (you must add pseudo-forces).

Myth: Normal = mg always

“A seatbelt works because your body obeys Newton's first law — it wants to keep moving when the car suddenly stops.”

True only on a horizontal surface with no other vertical forces.

Work

“A roller-coaster is an energy story: the first big climb 'loads' the potential energy that powers the whole ride.”

Energy transferred by a force: W = F·d·cosθ, where θ is the angle between force and displacement.

Memory trick: carrying a bag horizontally does no work against gravity, because the force is vertical.

Work — common mistake

“A roller-coaster is an energy story: the first big climb 'loads' the potential energy that powers the whole ride.”

A frequent error is forgetting the cosθ — a force perpendicular to the motion does zero work. In reality, energy transferred by a force: W = F·d·cosθ, where θ is the angle between force and displacement.

Memory trick: carrying a bag horizontally does no work against gravity, because the force is vertical.

Work–energy theorem

“A roller-coaster is an energy story: the first big climb 'loads' the potential energy that powers the whole ride.”

The net work done on a body equals its change in kinetic energy.

Memory trick: net work > 0 speeds a body up; net work < 0 slows it down.

Work–energy theorem — common mistake

“A roller-coaster is an energy story: the first big climb 'loads' the potential energy that powers the whole ride.”

A frequent error is using only one force's work instead of the net work. In reality, the net work done on a body equals its change in kinetic energy.

Memory trick: net work > 0 speeds a body up; net work < 0 slows it down.

Conservation of mechanical energy

“A roller-coaster is an energy story: the first big climb 'loads' the potential energy that powers the whole ride.”

When only conservative forces act, KE + PE stays constant.

Memory trick: if there's friction, account for the energy lost as heat.

Conservation of mechanical energy — common mistake

“A roller-coaster is an energy story: the first big climb 'loads' the potential energy that powers the whole ride.”

A frequent error is applying it when friction or other non-conservative forces are present. In reality, when only conservative forces act, KE + PE stays constant.

Memory trick: if there's friction, account for the energy lost as heat.

Power — common mistake

“A roller-coaster is an energy story: the first big climb 'loads' the potential energy that powers the whole ride.”

A frequent error is confusing power (how fast work is done) with energy (the total work). In reality, the rate of doing work, P = W/t = F·v.

Memory trick: a strong engine does the same work faster — more power, not more energy.

W = Fd cosθ

“A roller-coaster is an energy story: the first big climb 'loads' the potential energy that powers the whole ride.”

Work done by a constant force. Use it when the force is constant along the displacement.

W = Fd cosθ

KE = ½mv²

“A roller-coaster is an energy story: the first big climb 'loads' the potential energy that powers the whole ride.”

Kinetic energy of a moving body. Use it when always.

KE = ½mv²

P = Fv

“A roller-coaster is an energy story: the first big climb 'loads' the potential energy that powers the whole ride.”

Instantaneous power from force and velocity. Use it when force acts along velocity.

P = Fv

PE = ½kx²

“A roller-coaster is an energy story: the first big climb 'loads' the potential energy that powers the whole ride.”

Elastic potential energy stored in a stretched/compressed spring. Use it when the spring obeys Hooke's law.

PE = ½kx²

conservative force vs non-conservative force

“A roller-coaster is an energy story: the first big climb 'loads' the potential energy that powers the whole ride.”

A conservative force (gravity, spring) stores energy recoverably and does path-independent work; a non-conservative force (friction) dissipates energy and depends on the path.

energy vs power

“A roller-coaster is an energy story: the first big climb 'loads' the potential energy that powers the whole ride.”

Energy is the total capacity to do work (joules); power is how quickly that work is done (watts).

elastic collision vs inelastic collision

“A roller-coaster is an energy story: the first big climb 'loads' the potential energy that powers the whole ride.”

Both conserve momentum; an elastic collision also conserves kinetic energy, while an inelastic one converts some KE into heat/deformation.

Myth: Momentum lost in inelastic collisions

“A roller-coaster is an energy story: the first big climb 'loads' the potential energy that powers the whole ride.”

Momentum is always conserved in collisions — only kinetic energy is lost in inelastic ones.

Centre of mass — common mistake

“A figure skater spins faster by pulling their arms in — physics on ice, live.”

A frequent error is assuming it always lies inside the body (for a ring it's at the empty centre). In reality, the single point where the whole mass of a system can be treated as concentrated.

Memory trick: for symmetric bodies it sits at the geometric centre.

Torque — common mistake

“A figure skater spins faster by pulling their arms in — physics on ice, live.”

A frequent error is using the force alone instead of force times perpendicular (lever-arm) distance. In reality, the turning effect of a force, τ = r×F = rF·sinθ — the rotational analogue of force.

Memory trick: pushing a door far from the hinge needs less force — bigger lever arm.

Moment of inertia — common mistake

“A figure skater spins faster by pulling their arms in — physics on ice, live.”

A frequent error is treating it as a fixed property regardless of the axis chosen. In reality, the rotational analogue of mass; it depends on both the mass and how it is distributed about the axis.

Memory trick: mass far from the axis contributes much more (distance is squared).