A bicycle wheel of radius 0.28 m rolls down a hill without slipping. Its linear velocity increases constantly from 0 to 8 m/s in 2.6 s. What is its angular acceleration?

10.989 rad/s²

Explanation:

Angular Acceleration: This is the acceleration of a body that undergoes a circular motion. The S.I unit of angular acceleration is rad/s²

The expression for angular acceleration is given as

a = αr Equation 1

Where a = linear acceleration, α = angular acceleration, r = radius.

make α the subject of the equation

α = a/r Equation 2.

But,

a = (v-u)/t Equation 3

Where v = final velocity, u = initial velocity, t = time.

substitute equation 3 into equation 2

α = (v-u)/rt Equation 4

Given: v = 8 m/s, u = 0 m/s, r = 0.28 m, t = 2.6 s

Substitute into equation 4

α = (8-0)/(0.28×2.6)

α = 8/0.728

α = 10.989 rad/s²