Question

A wheel of radius 1.5 m. is rotating at a constant angular acceleration of 10 rad/s². Its initial angular speed is (60/π) rpm. What will be its angular speed and angular displacement at t=2.0 sec?

Answer 1

First, convert initial angular speed in rev/min to rad/s
60/π rpm = [(60/π) × 2 π rad]/(60 s) rad/s = 2 rad/s

ωf = ωi + αt
= 2 rad/s + (10 rad/s² × 2.0 s)
= 22 rad/s
Angular speed at t = 2.0 second is 22 rad/s

θ = (ωf² - ωi²) / (2 × α)
= [(22 rad/s)² - (2 rad/s)²] / (2 × 10 rad/s²)
= 24 rad
Angular displacement covered by wheel after 2.0 second is 24 rad