Motion In A Circle

Question 1

Define angular displacement, θ

Answer 1

Angular displacement is the angle of rotation of a body about an axis in a specific direction from a reference point.

Question 2

Define angular velocity, ω

Answer 2

Angular velocity is the rate of change of angular displacement of a body.

Question 3

Formula for angular velocity, ω

Answer 3

ω = Δθ/Δt
ω = 2π/t
ω = 2πf

Question 4

Formula for linear velocity, v

Answer 4

v = rω
(aka tangential velocity)

Question 5

Explain centripetal acceleration

Answer 5

Since the direction of this acceleration is radial and towards the centre of the circular path, this acceleration is called centripetal acceleration.

Question 6

Formula for centripetal acceleration

Answer 6

a = v²/r
a = rω².

Question 7

Explain centripetal force

Answer 7

According to Newton’s Second Law of Motion, for a body to move at constant speed in a circular path, it must have a resultant force acting on it to have a centripetal acceleration. This force is also known as the centripetal force, and acts in the direction is the centripetal acceleration towards the centre of the circular path.

Question 8

Formula for centripetal force

Answer 8

F = ma (a is centripetal accl.)
F = mv²/r (v is linear velocity)
F = mrω² (ω is angular velocity)