TOPIC 6: MOTION IN A CIRCLE

Question 1

[Definition] Angular Displacement, θ

Answer 1

Angular displacement is the angle swept out by a radius

Question 2

[Formula] Angular Displacement, θ

Answer 2

θ = s/r

θ: angular displacement (rad)
s: arc length (m)
r: radius (m)

Question 3

[Definition] Angular Velocity, ω

Answer 3

Angular velocity is the rate of change of angular displacement swept out by a radius

Question 4

[Definition] One radian

Answer 4

One radian is the angle subtended at the centre of a circle by an arc length that is equal to the radius

Question 5

[Formula] Angular Velocity, ω

Answer 5

ω = dθ/dt

Question 6

Finding frequency using angular velocity

Answer 6

ω = dθ/dt = 2π/T = 2πf

Question 7

Relationship between angular and linear

Answer 7

s = rθ
v = rω

Question 8

[Formula] Centripetal acceleration, ac

Answer 8

ac = v²/r
ac = rω²

Question 9

[Formula] Centripetal force, Fc

Answer 9

Fc = mv²/r
Fc = mrω²

Question 10

Why is there always no work done during circular motion by a centripetal force?

Answer 10

The force that provides the centripetal force for the object to undergo uniform circular motion is always perpendicular to the motion of the object.

So, as there is no displacement in the direction of the force, there is no work done.

Question 11

Linear/angular velocity/acceleration/momentum during circular motion

Answer 11

Linear velocity: Varying
Angular velocity: Constant
Linear acceleartion: Varying
Linear momentum: Varying