A potter's wheel having a radius 0.50 m and a moment of inertia of 10.1 kg · m2 is rotating freely at 51 rev/min. The potter can stop the wheel in 4.0 s by pressing a wet rag against the rim and exerting a radially inward force of 74 N. Find the effective coefficient of kinetic friction between the wheel and the wet rag.

The effective coefficient of kinetic friction =0.3644

Explanation:

Given Data:

r=0.50 m

I=moment of inertia = 10.1 kg · m^2

ω=51 rev/min=0.885 rev/sec

t=4.0 sec

F=74 N

Required:

the effective coefficient of kinetic friction between the wheel and the wet rag=?

Solution:

Angular Acceleration=α=2π*ω/t

Angular Acceleration=α=2π*0.85/4

Angular Acceleration=α=1.3351 rad/s^2

Torque=τ=μ*F*r=I*α

Where:

μ is co-officient of friction

μ

μ=

The effective coefficient of kinetic friction =0.3644

The effective coefficient of kinetic friction is 0.0682

Explanation:

The kinetic energy is equal to the frictional work:

Ek = W

Where

I = moment of inertia = 10.1 kg m²

w = angular velocity = 51 rev/min = 5.341 rad/s

(eq. 1)

The frictional work is:

(eq. 2)

The rotational expression of motion:

(eq. 3)

Where

R = radially inward force = 74 N

t = 4

Using eq. 1, 2 and 3:

speed of light in vacuum is 300,000 km/s

speed of light in other mediums is given by the expression v = c/n, where c is the speed of light in vacuum and n is the refractive index of medium.

for the first medium v = 200,000 km/s

  so, refractive index of medium = 300000/200000 = 1.5

    1.5 refractive index is usually for glass. so first medium is glass.

for the second medium v = 250,00 km/s

so, refractive index of medium = 300000/250000 = 1.2

    1.2 refractive index is usually for water. so second medium is water.

for the third medium v = 0 km/s

so, refractive index of medium = 300000/0 = ∞

    ∞ refractive index is usually for opaque mediums. so third medium is opaque medium.