Question

(c) The angular velocity of a disc of mass 3 kg and radius 0.6 m changes from 10 rev/s to 15 rev/s in 0.07 s. Calculate the impulse and the torque on the disc.

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Answer 1

To calculate the impulse and torque on the disc, we can use the following equations:

Impulse = change in momentum = m * (v2 - v1)
Torque = moment of inertia * angular acceleration

First, let's calculate the moment of inertia of the disc:

I = (1/2) * m * r^2
I = (1/2) * 3 kg * (0.6 m)^2
I = 0.54 kg * m^2

Next, let's calculate the angular acceleration:

alpha = (omega2 - omega1) / t
alpha = (15 rev/s - 10 rev/s) / 0.07 s
alpha = 71.4 rad/s^2

Now we can calculate the impulse:

Impulse = m * (v2 - v1)
Impulse = 3 kg * ((2 * pi * 0.6 m * 15 rev/s) - (2 * pi * 0.6 m * 10 rev/s))
Impulse = 113.1 Ns

Finally, we can calculate the torque:

Torque = moment of inertia * angular acceleration
Torque = 0.54 kg * m^2 * 71.4 rad/s^2
Torque = 38.6 Nm

Therefore, the impulse on the disc is 113.1 Ns and the torque on the disc is 38.6 Nm.