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 t. How much power is del

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Solution

Q.
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 $θ (t) = 5 t^{2} - 8 t$ , where $θ (t)$ is the angular position of the rotating disc as a function of time t. How much power is delivered by the applied torque, when t = 2 s [2025]

1 $60 M R^{2}$

2 $72 M R^{2}$

3 $108 M R^{2}$

4 $8 M R^{2}$

Ans.
(1)

Given: $θ = 5 t^{2} - 8 t$

$ω = \frac{d θ}{d t} = 10 t - 8$

$α = \frac{d ω}{d t} = 10 {rads}^{- 2}$

Power, $P = τ ω = (I α) ω$

$\Rightarrow P = (\frac{M R^{2}}{2}) α ω = (\frac{M R^{2}}{2}) (10) (10 t - 8)$

Put t = 2 s, $P = 60 M R^{2}$

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