Radial & Tangential Acceleration for Non Uniform Circular Motion
A car wheel r...
Question
A car wheel rotates with an angular acceleration α=4t3(in rad/s2) where t is the time taken (in seconds). If the wheel has initial angular velocity ω0=20rad/s, then the angular velocity ω(t) after 2s is
A
20rad/s
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B
36rad/s
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C
4rad/s
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D
16rad/s
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Solution
The correct option is B36rad/s Initial angular velocity w0=20rad/s
Given α=4t3 ∵α is a function of time dωdt=4t3 dω=4t3dt
Integrating on both sides, ∫ωω0dω=∫t04t3dt ω−ω0=[t4]20 ⇒ω=ω0+[t4]20 =20+16=36rad/s