A uniform disc of mass 2 kg and radius 1 m is acted upon by torque τ(t)=5t²-8t N m. The disc starts from rest. Find the power delivered by the torque at t=1 s.
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A uniform disc of mass 2 kg and radius 1 m is acted upon by torque τ(t)=5t²-8t N m. The disc starts from rest. Find the power delivered by the torque at t=1 s.

G1 Physics · Accepted Answer

For the disc, I=MR²/2=1 kg m². Hence α=τ/I=5t²-8t. Starting from rest, ω=∫₀ᵗ(5t²-8t)dt=(5/3)t³-4t². At t=1 s, τ=-3 N m and ω=5/3-4=-7/3 rad s⁻¹. Power P=τω=(-3)(-7/3)=7 W.