How Does Torque Affect the Stopping Time of a Potter's Wheel?

[big_sur]

A potter is shaping a bowl on a potters wheel rotating at constant angular speed. The frictional force between her hands and the clay is 1.5N total. A. How large is her torque on the wheel, if the diameter of the bowl is 12 cm? B. How long would it take for the potters wheel to stop if the only torque acting on it is due to the potters hand? The initial angular velocity of the wheel is 1.6 rev\s, and th moment of inertia of the wheel and the bowl is 0.11kg*m^2.

So part A is just the force times the radius right? ie. 1.5N*.06m=.09Nm. Part B is my sticking point. I'm not really sure where to go from here.

 

[Nate810]

For Part B, you need to use the equation for torque: Torque = Moment of Inertia x Angular AccelerationYou can rearrange this equation to solve for the angular acceleration given the torque and the moment of inertia. Then, use the equation for angular velocity given angular acceleration and initial angular velocity to solve for the time it takes for the wheel to stop.

 

[ogb p]

Yes, part A is correct. The torque is equal to the force applied multiplied by the distance from the axis of rotation (in this case, the radius of the wheel).

For part B, we can use the equation for rotational motion: τ = Iα, where τ is the torque, I is the moment of inertia, and α is the angular acceleration. Since the wheel is rotating at a constant angular speed, the angular acceleration is 0, so the torque is also 0. This means that the only torque acting on the wheel is due to the frictional force between the potter's hands and the clay.

To find the time it takes for the wheel to stop, we can use the equation ω = ω0 + αt, where ω is the final angular velocity, ω0 is the initial angular velocity, α is the angular acceleration, and t is the time. Since α is 0, this equation simplifies to ω = ω0, which means that the final angular velocity is equal to the initial angular velocity. We can plug in the values given in the question to get:

1.6 rev/s = ω0

ω0 = 1.6 rev/s * (2π rad/rev) = 10.08 rad/s

Now, we can use the equation ω = ω0 + αt to solve for t:

0 = 10.08 rad/s + 0 * t

t = -10.08 rad/s / 0 = undefined

Since the angular acceleration is 0, the wheel will never stop rotating. It will continue to rotate at a constant angular speed of 1.6 rev/s.