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Chapter 9: Q.72 (page 230)

A uniform solid bar with mass m and length L rotates with angular velocity v about an axle at one end of the bar. What is the bar’s kinetic energy?

Short Answer

Expert verified

The total kinetic energy of the bar is16(mω2L2).

Step by step solution

01

Content Introduction

The formula to find kinetic energy for the small element of bar is

dK=12v2dm

here,dKis the kinetic energy of the small element of bar,vis linear velocity,dmis mass element of the same.

02

Content Explanation

Integrate the kinetic energy of each small element of the bar to find the total kinetic energy,

K=∫0LdKK=∫0L12v2dmK=∫0L12(ωx)2dm

The formula to find the small mass is

dm=λdx

Substitute

K=∫0L12(ωx)2dmK=12ω2λ∫0L(x)2dxK=16ω2λL3K=16mω2L2

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