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Question

A wheel rotates with a constant angular acceleration of 3.6 rad/s2. If angular velocity of the wheel is 4.0 rad/s at time t0=0, what angle does the wheel rotate in 1 s? What will be its angular velocity at t=1 s?

A
θ=5.8 rad,ω=0.4 rad/s
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B
θ=2.2 rad,ω=0.4 rad/s
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C
θ=5.8 rad,ω=7.6 rad/s
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D
θ=2.2 rad,ω=7.6 rad/s
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Solution

The correct option is C θ=5.8 rad,ω=7.6 rad/s
Given,
Angular acceleration α=3.6 rad/s2
Angular velocity of wheel at t0=0, ω0=4.0 rad/s
Angle rotated in 1 second from eq. θ=ω0t+12αt2
θ=4 (rad/s)×1 (s)+12×(3.6 rad/s2)×1× (s)2
θ=5.8 rad
From eqn. ω=ω0+αt, angular velocity at t=1 s
ω=4 (rad/s)+3.6 (rad/s2)×1 (s)
ω=7.6 rad/s

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