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Question

A wheel is at rest. Its angular velocity increases uniformly and becomes 80 radians second after 5 seconds. the total angular displacement is:


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Solution

Step 1: Concept used

The angular velocity (ω) is assumed to rise evenly.

The angular acceleration (α) must always be the same.

Given that it begins at rest and that the total angular velocity is80 rad/sec in 5 seconds,
ωi=0

ωf=80rad/sec

t=5sec

Step 2: Calculation of circular motion

By the equation of circular motion,

ωf=ωi+αt

α=805

=16rad/sec2

Step 3: Find the total angular displacement

The expression to find the angular displacement is given as :

θ=12αt2

=12×16×25

=200radas(ωo=0)

Therefore, the total angular displacement is 200rad.


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