The wheel of a motor, accelerated uniformly from rest, rotates through 5 radians during the first second. Calculate the angle rotated during the next second.

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Solution

As the angular acceleration is constant, we have
$θ ω_{0} t + \frac{1}{2} α t^{2} = \frac{1}{2} α t^{2}$
Thus, 5 rad = $\frac{1}{2} α (1 s) 62$
$α = 10 r a d / s^{2}$ or $α = 10 r a d / s^{2}$
The angle rotated during the first two seconds is
$= \frac{1}{2} \times (10 r a d / s^{2}) (2 s)^{2} = 20 r a d$ .
Thus, the angle rotated during the 2nd second is
$20 r a d - 5 r a d = 15 r a d$ .

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The wheel of a motor, accelerated uniformly from rest, rotates through 5 radians during the first second. Calculate the angle rotated during the next second.

As the angular acceleration is constant, we haveθω0t+12αt2=12αt2Thus, 5 rad = 12α(1s)62α=10rad/s2 or α=10rad/s2The angle rotated during the first two seconds is=12×(10rad/s2)(2s)2=20rad.Thus, the angle rotated during the 2nd second is20rad−5rad=15rad.