Circular Motion

What is a radian?

The angle subtended at the centre of a circle by an arc equal in length to the radius.

How many radians are in a full circle?

2π radians.

How do you convert degrees to radians?

Angle in degrees ÷ 360 × 2π.

Define the period of circular motion

Time taken for one complete revolution.

What is the unit of period?

Seconds (s).

Define frequency in circular motion

Number of complete revolutions per second.

What is the unit of frequency?

Hertz (Hz).

State the relationship between frequency and period

f = 1/T.

Define angular velocity

Rate of change of angular displacement.

State the angular velocity equation

ω = θ / t.

What is the unit of angular velocity?

Radians per second (rad s⁻¹).

Angular velocity in terms of period

ω = 2π / T.

Angular velocity in terms of frequency

ω = 2πf.

Define centripetal force

The resultant force acting towards the centre of a circle.

Why is a force required for circular motion?

Because velocity direction is constantly changing.

In what direction does centripetal force act?

Perpendicular to velocity, towards the centre.

State the linear speed equation for circular motion

v = rω.

Alternative speed equation using period

v = 2πr / T.

State the centripetal acceleration equation

a = v² / r.

Centripetal acceleration in terms of angular velocity

a = rω².

State the centripetal force equation

F = mv² / r.

Centripetal force in terms of angular velocity

F = mrω².

What provides centripetal force in planetary orbits?

Gravitational force.

What provides centripetal force in a car turning a corner?

Friction.

What provides centripetal force for a mass on a string?

Tension.

Key idea about centripetal force

It is the resultant inward force, not a separate force.

What happens if centripetal force is removed?

Object moves tangentially.

Describe the circular motion practical with a bung

Bung on string through tube with hanging mass.

What provides the centripetal force in the bung experiment?

Weight of the hanging mass (Mg).

Why is the tension equal to Mg?

String is in equilibrium vertically.

What is measured in the bung experiment?

Time for revolutions and radius.

How is speed found in the bung experiment?

v = 2πr / T.

Equation linking centripetal force and hanging mass

Mg = mv² / r.

What graph is plotted in the bung experiment?

v² against M.

What is the expected shape of the graph?

Straight line through the origin.

Why must the radius be kept constant?

To ensure fair test conditions.

Why repeat measurements in circular motion experiments?

To improve reliability.