6: Motion in a Circle

Question 1

Angular Displacement, θ

Answer 1

Angular displacement is defined as the angle through which an object turns with respect to the centre of the circular path. [rad]

Question 2

Angular displacement, θ formula

Answer 2

θ = s/r

s - arc length
r - radius

Question 3

Angular velocity, ω

Answer 3

Angular velocity is the rate of change with time of the angular displacement (θ) of a radius joining an object to the axis about which it is rotating.

Question 4

Angular velocity, ω formula

Answer 4

ω = dθ/dt

ω = 2π/T = 2πf

Question 5

R/s between angular velocity (ω) and linear velocity (v)

Answer 5

v = rω

Question 6

Centripetal acceleration, (aç) formula

Answer 6

aç = v²/r = rω²

Question 7

Centripetal force, Fc formula

Answer 7

Fc = mrω² = mvω

Question 8

Horizontal circular motion:

• Fc provided by ____
• F(resultant) = _______

Answer 8

• Fc is provided by T

- F(resultant) = T = Fc

Question 9

Vertical circular motion:

• Fc provided by _________
• F(resultant) = __________

Answer 9

• Fc is provided by result of N + W

- F(resultant) = N + W = Fc