Chapter 12. Circular Motion

Question 1

Define the radian and its formula.

Answer 1

The angle subtended at the centre of a circle by an arc length equal to the radius of the circle.
θ = arc length(s) / radius (r)

Question 2

What is angular displacement and its unit and symbol?

Answer 2

The angle swept out by the radius at the centre of a circle.Symbol is θ in rad

Question 3

What is angular speed and its unit and symbol?

Answer 3

The angle swept out by the radius per unit time. Symbol is ω in rads^-1.

Question 4

Convert 45⁰ to radians.

Answer 4

θ = (45/180) * π

Question 5

Define period.

Answer 5

The time taken to complete one revolution.

Question 6

Derive the formula for linear velocity of circular motion.

Answer 6

1. △θ = △s/r so △s = △θr
2. △s/△t = △θr/△t
3. since △s/△t = v and △θ/△t = ω it is therefore that :
4. v = ωr

Question 7

What are the requirements for a system to be in equilibrium?

Answer 7

1. No resultant force
2. No resultant moment

Question 8

What is the formula for centripetal acceleration?

Answer 8

a = ω²r or a = v²/r
N.B Knowing how to derive this from similar triangles will prove to be useful.

Question 9

What is the formula for angular displacement of a full circle?

Answer 9

ω = 2π/T, where T is the period.