Question

# A wheel rotates with a constant angular acceleration of $2 rad s^{-2}$. If the wheel starts from rest, number of revolutions it makes in first 10 seconds will be approximately:A. 32B. 24C. 16D. 8

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Hint: When the wheel starts rotation with an acceleration, its angular velocity will increase with time. Hence in such cases, we have to use the equations of motion for circular motion. Further, one revolution means 2π radians. Hence we can convert the number of rotations into radians rotated by multiplying it by 2π and vice-versa.

Formula used: $\theta = \omega_{\circ}t + \dfrac 12 \alpha t^2$, where $\omega_{\circ }$ is the initial angular velocity of the body and $\alpha$ is the angular acceleration and $\theta$ is the angle ( in radian) rotated by the body in time ‘t’.

Given $\omega_{\circ }$= 0 as the body starts from rest.
t=10 sec and $\alpha$=$2 rad s^{-2}$
Putting the values in the equation: $\theta = \omega_{\circ}t + \dfrac 12 \alpha t^2$, we get
$\theta = (0)\times 10 + \dfrac 12 2 (10)^2 = 100 rad$
$No.\ of\ revolutions\ = \dfrac{100}{2\pi} = 15.9$