A rope is wrapped around the rim of a large uniform solid disk of mass 325 kg and radius 3.00 m. The horizontal disk is made to rotate by pulling on the rope with a constant force of 195 N. If the disk starts from rest, what is its angular speed in rev/s at the end of 2.05 s?

The angular speed is 0.13 rev/s

Explanation:

From the formula

Where is the torque

is the moment of inertia

is the angular acceleration

But, the angular acceleration is given by

Where is the angular speed

and is time

Then, we can write that

Hence,

Now, to determine the angular speed, we first determine the Torque and the moment of inertia .

Here, The torque is given by,

Where r is the radius

and F is the force

From the question

r = 3.00 m

F = 195 N

∴

Nm

For the moment of inertia,

The moment of inertia of the solid disk is given by

Where M is the mass and

R is the radius

∴

kgm²

From the question, time t = 2.05 s.

Putting the values into the equation,

rad/s

Now, we will convert from rad/s to rev/s. To do that, we will divide our answer by 2π

0.82 rad/s = 0.82/2π rev/s

= 0.13 rev/s

Hence, the angular speed is 0.13 rev/s,

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