Question

A 35 cm -diameter potter's wheel with a mass of 15 kg is spinning at 180 rpm. Using her hands, a potter forms a 14 cm-diameter pot that is centered on and attached to the wheel. The pot's mass is negligible compared to that of the wheel. As the pot spins, the potter's hands apply a net frictional force of 1.3 N to the edge of the pot. If the power goes out, so that the wheel's motor no longer provides any torque, how long will it take the wheel to come to a stop? You can assume that the wheel rotates on frictionless bearings and that the potter keeps her hands on the pot as it slows. Express your answer to two significant figures and include the appropriate units.

Answer 1

given,

diameter of the wheel = 35 cm

diameter of the pot = 14 cm

mass of wheel = 15 kg

angular speed of the wheel = 180 rpm or 18.849 rad/sec

torque = force * distance

distance = 14 / 2 cm or 7 cm

torque applied = 1.3 * 0.07

torque = moment of inertia * angular acceleration

moment of inertia of wheel = 0.5 * mass * radius^2

1.3 * 0.07 = 0.5 * 15 * 0.175^2 * angular acceleration

angular acceleration = 0.3962 rad/sec^2

final velocity of the wheel = 0 rad/sec as it is stopping at the end

by first equation of motion

v = u + at

acceleration will be negatice since it is stoping the wheel

0 = 18.849 - 0.3962 * time

time = 47.5744 sec

time taken by wheen to stop = 47.5744 sec