Question

You balance a disc (imagine a plate or a frisbee) on the tip of your finger and spin it so

that it is spinning at a rate of four rotations a second. When you leave it alone, in time T, it slows down
to a rate of one rotation per second. The disc has mass M and radius R.
A. What is the angular acceleration? (choose axes, and give the magnitude and direction of the angular
acceleration).
B. What angle does the disc rotate through in this time?
C. How much work is done in slowing it down?

Answer 1

To find the work done on a spinning object, such as a frisbee or a grindstone, one must calculate the product of the force applied and the arc length traveled. The formula used is net W = (net F)As, and the work done must account for the specific rotation (in radians) and net force applied perpendicular to the radius.

Step-by-step explanation:

When calculating the work and energy associated with spinning objects such as grindstones or frisbees, we apply the principles of rotational motion. Work in rotational motion is given by the net work done as the product of the force times the arc length traveled, which is net W = (net F)As, where net F is the net force exerted perpendicular to the radius and As is the arc length.

For example, if a person exerts a force of 200 N through a rotation of 1.00 rad (57.3°) on the edge of a grindstone with a 0.320-meter radius, the work done is found using the formula for the work in rotational motion. Assuming negligible friction, the work done translates into the change in rotational kinetic energy of the system. This work can be equated with the rotational kinetic energy gained by the object.