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

Question

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 $t = 2 s$ ?

TestHub · Accepted Answer

​ θ = 5 t 2 − 8 t ω = dt d θ ​ = 10 t − 8 α = dt d ω ​ = 10 ∴ p = τ ω = ( I α ) ω = ( 2 mR 2 ​ ) α ω = ( 2 mR 2 ​ ) ( 10 ) ( 10 ​ Put t = 2 p = 60 mR 2

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