An object is placed on a rotating disk. The amount of time it takes the object to make one revolution around the center of the circle may be set at a known value. Which of the following procedures could be used to make the necessary measurements to find the coefficient of static friction between the object and the disk’s surface?

Place the object on the disk and measure the distance from the center of the disk to the center of mass of the object by using a meterstick. Slowly increase the rate the disk rotates until the object begins to slide off the disk. Record the time in which the object makes one revolution around the center of the disk.

Explanation:

Draw a free body diagram.  There are three forces:

Weight force mg pulling down,

Normal force N pushing up,

Friction force Nμ pushing towards the center.

Sum of forces in the vertical direction:

∑F = ma

N − mg = 0

N = mg

Sum of forces in the centripetal direction:

∑F = ma

Nμ = m v²/r

mgμ = m v²/r

gμ = v²/r

μ = v² / (gr)

It takes T seconds for the object to move 2πr meters.

v = 2πr / T

Substituting:

μ = (2πr / T)² / (gr)

μ = 4π²r / (gT²)

The measurements you need are the distance between the object and the center of the disk (r) and the time it takes for one revolution (T).