Circular Motion

How do you convert degrees to radians?

Multiply by π/180.

How do you convert radians to degrees?

Multiply by 180/π.

What are 360°, 180° and 90° in radians?

360° = 2π rad; 180° = π rad; 90° = π/2 rad.

What is the time period, T?

The time taken for one complete revolution, measured in seconds.

What is the relationship between time period and frequency?

T = 1/f and f = 1/T. Frequency is measured in Hz.

What is the equation for linear speed in circular motion?

v = 2πr/T = 2πrf.

What is angular velocity, ω?

Angular displacement per unit time, measured in rad s⁻¹.

What are the equations for angular velocity?

ω = 2π/T = 2πf.

How are linear speed and angular velocity related?

v = ωr.

How do you convert RPM to rad s⁻¹?

ω = RPM × 2π/60.

A wheel spins at 120 RPM. Find its angular velocity.

ω = 120 × 2π/60 = 4π ≈ 12.6 rad s⁻¹.

What is centripetal force?

The resultant force directed towards the centre that maintains circular motion.

What is the direction of centripetal force?

Towards the centre, perpendicular to the instantaneous velocity.

What is the equation for centripetal force?

F = mv²/r = mω²r.

What is the equation for centripetal acceleration?

a = v²/r = ω²r.

What provides the centripetal force?

A resultant force such as tension, gravity, friction or normal reaction.

Why does an object accelerate at constant speed in a circle?

Its velocity direction continuously changes, so its velocity changes.

Why can centripetal force change velocity without changing speed?

It acts perpendicular to velocity, changing direction but not magnitude.

Why does centripetal force do no work in uniform circular motion?

Force is perpendicular to displacement, so W = Fs cos 90° = 0.

What is the gradient of an F against v² graph?

Gradient = m/r.