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Question

A wheel whose moment of inertia is 12kgm2 has an initial angular velocity of 40rad/s. A constant torque of 20Nm acts on the wheel. The time in which the wheel is accelerated to 100rad/s is


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Solution

Step 1: Given information

Torque, T=20Nm

Moment of inertia, I=12kgm2

Step 2: To find

We have to find the time to which the wheel is accelerated to 100rad/s.

Step 3: Calculation

Calculate the acceleration using the formula,

T=Iα...1

Where, T is the torque, α is the acceleration, and

Substitute the values in equation (1).

20=12×αα=2012

Use the first equation of motion,

ω=ωo+αt

Where, ωo is the initial velocity, and ω is the final velocity, and t is the time.

ω0=40ω=ω0+αt100=40+2012tt=60×1220t=36sec

Therefore, the time in which the wheel is accelerated to 100rad/s is 36seconds.


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