A wheel undergoes a constant angular acceleration from time t=0 to t=20 s and thereafter angular acceleration is zero. If angular velocity at t=2 s is…

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A wheel undergoes a constant angular acceleration from time t=0 to t=20 s and thereafter angular acceleration is zero. If angular velocity at t=2 s is found to be 5 rad/s, then the number of revolutions made by the wheel in time interval t=0 s to t=50 s is

MARKS Content Team · Accepted Answer

Correct answer: (A) 1000/π. From kinematic equations of circular motion, we have ω=ω_0+αt ⇒5=0+α×2 ⇒α=2.5 rad s^(-2) For total angle rotated, we have θ=θ1_(0 to 20 s)+θ2_(20 to 50 s) ⇒θ=ω_0×20+1/2α×20^2+ω×30, here ω is angular velocity at t=20 s ⇒θ=ω_0×20+1/2×α×20^2+ω_0+α×20×30 ⇒θ=0×20+1/2×2.5×20^2+0+2.5×20×30 ⇒θ=500+1500=2000 ⇒n×2π=2000 ⇒n=1000/(π)

A wheel undergoes a constant angular acceleration from time $t = 0$ to $t = 20 s$ and thereafter angular acceleration is zero. If angular velocity at $t = 2 s$ is found to be $5 rad / s,$ then the number of revolutions made by the wheel in time interval $t = 0 s$ to $t = 50 s$ is

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