The rotational velocity of a wheel increases from 0 rad/s to 4.5 rad/s in a time

Question

The rotational velocity of a wheel increases from 0 rad/s to 4.5 rad/s in a time of 6.0 sec. What is the rotational acceleration of the wheel? A merry-go-round is accelerated from rest at a constant rate of 0.8 rad/s^2 a. What is the rotational speed of the merry-go-round after 3 seconds? b. Through what angle will if have turned in this time? c. If the mass of it 600kg and radius 1.5m, calculate I and L. A merry-go-round in the park has a radius of r = 1.8 m and rotational inertia of I = 900 kg m^2. A child pushes the merry-go-round with a constant force of F = 80 N applied at edge and parallel to the edge. a. What is the net torque (tau) acting on the merry-go-round about its axle? b. What is the rotational acceleration (alpha) of the merry-go-round?

Explanation / Answer

Question 1) since 1 revolution = 2 radians

And 1 minute = 60 seconds

So 1 rpm =( 2/60) rad/s

Given 1200 rpm

So,

1200 rpm = (1200*2/60) rad/s = 125.6637 rad /s

Therefore, 1200 rpm = 125.6637 rad/s

Question 2) given , wf = 4.5 rad/s , wi = 0

time = 6 s

Angular acceleration = (wf - wi)/t

Angular acceleration = 4.5/6 = 0.75 rad/s^2

Therefore, rotational acceleration = 0.75 rad/s^2

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