Question

A horizontal disk of diameter 40 cm is spinning around its axis. A 1.6-g bug is on top of the disk, at the outer edge, hanging on to keep from being thrown off. Where the bug is located, its rotational speed is 70 cm/s.

a) Taking as your reference point a spot behind the bug as it rotates (so the velocity is away from you, into the page), draw a free-body diagram of the bug showing all forces, the presumed direction of acceleration (if any), and an appropriate choice of x−y axes.
b) Apply Newton's Second Law to the free body diagram, write equations relating the forces, mass, and acceleration, as taught in this unit.
c) Solve the relevant equations to find the friction force acting on the bug, in Newtons (N). State explicitly whether this force is static or kinetic.
d) Assuming the bug is just on the verge of sliding, find the coefficient of friction between the bug and the disk.

Answer 1

To solve the problem, one must draw a free-body diagram for the bug, apply Newton's Second Law to find the friction force, identify the type of friction, and then use that to find the coefficient of friction.

Step-by-step explanation:

The problem described involves a rotational motion scenario in which a bug is clinging onto a spinning disk. To address this question:

• A free-body diagram must be sketched, showing forces such as the normal force exerted by the disk on the bug, the gravitational force acting on the bug, and the frictional force that provides the centripetal force necessary to keep the bug in circular motion.
• Applying Newton's Second Law in the radial direction, we can equate the centripetal force necessary for circular motion to the frictional force. With the mass of the bug and its velocity, this allows us to calculate the magnitude of the frictional force.
• The type of frictional force, whether it is static or kinetic, depends on whether the bug is sliding or not. In this case, since it is on the verge of sliding but still stationary relative to the disk, we assume it is static friction.
• Finally, calculating the coefficient of friction involves dividing the frictional force by the product of the normal force and the gravitational force acting on the bug.

This problem demonstrates the application of concepts of forces in rotational motion and provides insight into how friction enables circular motion.