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A wheel having a diameter of 3 m starts from rest and accelerates uniformly to an angular velocity of 210 r.p.m. in 5 seconds. Angular acceleration of the wheel is:

1. 4.4 rad \( s^{-2} \)
2. 3.3 rad \( s^{-2} \)
3. 2.2 rad \( s^{-2} \)
4. 1.1 rad \( s^{-2} \)

Correct answer: 4.4 rad \( s^{-2} \)

Solution

The wheel starts from rest, so its angular acceleration is the final angular velocity divided by the time taken. Converting 210 rpm to rad/s gives about 22 rad/s, and dividing by 5 s gives about 4.4 rad/s².

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