Question

A wheel of diameter 40cm started from rest and attains a speed of 240 RPM in 4 minute calculate its angular displacement within this time interval​

Answer 1

The angular displacement within this time interval​ will be 3014.4 radians

Explanation :

Initial angular velocity, ω₀ = 0

Final angular velocity, ω = 2πN/60

=> ω = 2 x 3.14 x 240/60 = 25.12 rad/sec

Given time t = 4 min = 240 sec

From the law of angular motion,

ω = ω₀ + αt

=> 25.12 = 0 + 240α

=> α = 25.12/240

Hence Angular displacement,

θ = ω₀t + αt²/2

=> θ = 0 + 25.12/240  x 240 x 240 x 0.5

= 3014.4 radians

Hence the angular displacement within this time interval​ will be 3014.4 radians