Question 147 of 280
A circular disk of radius R meter and mass M kg is rotating around the axis perpendicular to the disk. An external torque is applied to the disk such that , where is the angular position of the rotating disc as a function of time .
How much power is delivered by the applied torque, when ?
Show answer and solution
Answer: (D)
$\begin{aligned}
& \theta=5 \mathrm{t}^2-8 \mathrm{t} \\
& \omega=\frac{\mathrm{d} \theta}{\mathrm{dt}}=10 \mathrm{t}-8 \\
& \alpha=\frac{\mathrm{d} \omega}{\mathrm{dt}}=10 \\
& \therefore \mathrm{p}=\tau \omega \\
& =(\mathrm{I} \alpha) \omega \\
& =\left(\frac{\mathrm{mR}^2}{2}\right) \alpha \omega \\
& =\left(\frac{\mathrm{mR}^2}{2}\right)(10)(10
\end{aligned}$
Put
& \theta=5 \mathrm{t}^2-8 \mathrm{t} \\
& \omega=\frac{\mathrm{d} \theta}{\mathrm{dt}}=10 \mathrm{t}-8 \\
& \alpha=\frac{\mathrm{d} \omega}{\mathrm{dt}}=10 \\
& \therefore \mathrm{p}=\tau \omega \\
& =(\mathrm{I} \alpha) \omega \\
& =\left(\frac{\mathrm{mR}^2}{2}\right) \alpha \omega \\
& =\left(\frac{\mathrm{mR}^2}{2}\right)(10)(10
\end{aligned}$
Put