A disc of mass 10 kg and radius 0 ⋅ 1 m is rotating at 120 r.p.m. A retarding torque brings it to rest in 10 s . If the same torque is due to force applied tangentially on the rim of the disc then mag

Question

A disc of mass 10 kg and radius 0 ⋅ 1 m is rotating at 120 r.p.m. A retarding torque brings it to rest in 10 s . If the same torque is due to force applied tangentially on the rim of the disc then magnitude of force is

TestHub · Accepted Answer

frequency f = 120 rpm = 60 120 ​ = 2 rps ω = 2 π f = 2 π × 2 = 4 π rad / s Angular acceleration =∝= t ω 2 ​ − ω 1 ​ ​ = 10 0 − 4 π ​ = 5 − 2 π ​ rad / s 2 Moment of inertia I = 2 MR 2 ​ = 2 10 × ( 0.1 ) 2 ​ = 0.05 kg m 2 Torque τ = I α = 0.05 × 5 2 ​ π = 0.02 π Nm . τ = Fr ∴ F = r τ ​ = 0.1 0.02 π ​ = 0.2 π N

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