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18 May, 06:22

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?

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  1. 18 May, 06:36
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    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
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