Question

a jeweler's grinding wheel slows down at a constant rate from 185 rad/s to 105 rad/s while it rotates through 16.0 revolutions. how much time does this take? express your answer with the appropriate units.

Answer 1

The jeweler's grinding wheel takes approximately 47.895 seconds to slow down from 185 rad/s to 105 rad/s while rotating through 16.0 revolutions.

Step-by-step explanation:

The jeweler's grinding wheel slows down at a constant rate from 185 rad/s to 105 rad/s while it rotates through 16.0 revolutions. To find the time it takes for this to occur, we need to use the formula:

Δω = α * Δt

Where Δω is the change in angular velocity, α is the angular acceleration, and Δt is the change in time. Since the angular acceleration is constant, we can rearrange the equation to solve for Δt:

Δt = Δω / α

First, let's find the change in angular velocity:

Δω = 105 rad/s - 185 rad/s = -80 rad/s

Next, we need the angular acceleration. Since it's a constant rate of change, we can use the formula:

α = (final angular velocity - initial angular velocity) / time

Solving for time:

Δt = Δω / α = -80 rad/s / α = (-80 rad/s) / ((105 rad/s - 185 rad/s) / (16.0 revolutions * 2π radians/revolution))

Converting revolutions to radians:

Δt = (-80 rad/s) / ((105 rad/s - 185 rad/s) / (16.0 * 2π radians))

Calculating the time:

Δt = (-80 rad/s) / ((105 rad/s - 185 rad/s) / (16.0 * 2 * 3.14159 radians)) = 47.895 seconds

So, it takes approximately 47.895 seconds for the jeweler's grinding wheel to slow down from 185 rad/s to 105 rad/s while rotating through 16.0 revolutions.