C16 Circular Motion

Question 1

Angular Velocity Formulae

Answer 1

ω = θ / t
ω = 2πf (given)
ω = 2π / T (given)

Question 2

Linear velocity of an object

Answer 2

v = 2πr / T (distance over time)
v = ωr (given)

Question 3

Unit for angular velocity

Answer 3

Radians per second, rad^-1

Question 4

Formula to calculate centripetal acceleration

Answer 4

a = v^2 / r (given)
a = ω^2 x r (given)

Question 5

Define Centripetal Acceleration

Answer 5

The acceleration of an object travelling in a circular path at a constant speed.

Question 6

Formulae for centripetal force

Answer 6

F = mv^2 / r (given)
F = m ω^2 r (given)

• Always acts toward the centre of the circular path, perpendicular to the direction of travel.

Question 7

Examples of centripetal forces which make objects follow circular paths

Answer 7

• Friction, on a bend.
• Tension, when swinging an object.
• Gravitational force, on a satellite.

Question 8

Why are banked tracks used in high-speed sports?

Answer 8

When the track is banked at an angle, the normal force of the object against the ground now has a horizontal component, which increases the overall centripetal force.

Question 9

Explain why you may feel lighter at the top of a ferris wheel, and heavier at the bottom.

Answer 9

When following a circular path, there must be a centripetal force in order for you to stay on this path. At the top of a ferris wheel, the net force must point downward, so the normal force is reduced, making you ‘feel’ lighter.