Question

After a jeweler's polishing wheel is unplugged it rotates to a complete stop in 77.46seconds t . The wheel slows down wich a constant angular velocity of the jeweler's polishing wheel has a magnitude of 0.500 before it was unplugged?

Answer 1

The angular velocity of the wheel before it was unplugged is 0.500 rad/s. The time it takes for the wheel to come to a complete stop is 77.46 seconds. The wheel makes 38.76 turns before coming to rest.

Step-by-step explanation:

The question asks about the angular velocity and the time it takes for a jeweler's polishing wheel to stop rotating after it is unplugged. The angular velocity of the wheel before it was unplugged is 0.500 rad/s. The time it takes for the wheel to come to a complete stop is given as 77.46 seconds.

We can use the formula:

Angular acceleration = (final angular velocity - initial angular velocity) / time

Substituting in the given values:

Angular acceleration = (0 - 0.500) / 77.46 = -0.00645 rad/s²

This negative value indicates that the wheel is slowing down.

To find the number of turns the wheel makes before coming to rest, we can use the formula:

Number of turns = (initial angular velocity)^2 / (2 * angular acceleration)

Substituting in the given values:

Number of turns = (0.500)^2 / (2 * -0.00645) = 38.76 turns