Physics CAPE

Purpose of dimensional analysis

To check correctness of equations.

Moment of a force

Turning effect of a force about a pivot.

Formula for moment

Moment = Force × perpendicular distance.

Unit of moment

N m.

Principle of moments

For equilibrium, sum of clockwise moments = sum of anticlockwise moments.

Condition for equilibrium (forces)

Resultant force = 0.

Condition for equilibrium (moments)

Resultant moment = 0.

Momentum

Product of mass and velocity.

Formula for momentum

p = mv.

Unit of momentum

kg m s⁻¹.

Impulse

Change in momentum.

Impulse formula

Impulse = Ft = mv − mu.

Law of conservation of momentum

Total momentum before collision = total momentum after collision.

Newton’s First Law

A body remains at rest or moves with constant velocity unless acted on by a net force.

Newton’s Second Law

Rate of change of momentum is proportional to applied force (F = ma).

Newton’s Third Law

For every action there is an equal and opposite reaction.

Component of weight down plane

mg sinθ.

Component of weight perpendicular to plane

mg cosθ.

Friction formula

F = μR.

Normal reaction on incline

R = mg cosθ.

Centripetal force

Force that keeps an object moving in a circular path.

Direction of centripetal force

Towards the centre of the circle.

Centripetal force formula

F = mv² / r.

Newton’s law of gravitation

Gravitational force between two masses is proportional to product of masses and inversely proportional to square of distance.

Gravitational force formula

F = Gm₁m₂ / r².

Weight equation

W = mg.

Projectile

Object moving under gravity only after projection.

Horizontal velocity in projectile motion

Constant.

Vertical acceleration in projectile motion

g.

Equation (v)

v = u + at.

Equation (s)

s = ut + ½at².

Equation (v²)

v² = u² + 2as.

Scalar quantity

Quantity with magnitude only.

Vector quantity

Quantity with magnitude and direction.

Resultant vector

Single vector with same effect as multiple vectors.

Horizontal component of a vector

V cosθ.

Vertical component of a vector

V sinθ.

Magnitude of resultant (perpendicular vectors)

√(a² + b²).

Simple harmonic motion

Motion where acceleration is proportional to displacement and directed towards equilibrium.

Amplitude

Maximum displacement from equilibrium.

Period

Time for one complete oscillation.

Frequency

Number of oscillations per second.

Angular frequency

ω = 2πf.

SHM acceleration equation

a = −ω²x.

Damping

Reduction in amplitude due to energy loss.

Free damping

Damping with no external driving force.

Light damping

Amplitude decreases slowly.

Critical damping

Returns to equilibrium in shortest time without oscillating.

Heavy damping

Returns to equilibrium slowly without oscillating.

Resonance

Maximum amplitude occurs when driving frequency equals natural frequency.

Natural frequency

Frequency at which a system oscillates freely.

Homogeneous equation

Equation where dimensions are same on both sides.

Base quantities

Length, mass, time, current, temperature, amount of substance, luminous intensity.