   Chapter 8, Problem 42P

Chapter
Section
Textbook Problem

A potter’s wheel having a radius of 0.50 m and a moment of inertia of 12 kg - m2 is rotating freely at 50 rev/min. The potter can stop the wheel in 6.0 s by pressing a wet rag against the rim and exerting a radially inward force of 70 N. Find the effective coefficient of kinetic friction between the wheel and the wet rag.

To determine
The effective coefficient of kinetic friction between the wheel and the wet rag.

Explanation

Given info: The moment of inertia of the wheel is 12kgm2 , the initial angular velocity of the wheel is 50rev/min , the radius of the wheel is 0.50m , and the time duration for the wheel to come rest is 6.0s .

Explanation: The torque of the wheel is τ=rf=Iα and the angular acceleration of the wheel is defined as α=ωi/Δt since its final angular velocity is zero (ωf=0rad/s) . Similarly, the force of friction is μn . Using these relations, the effective coefficient of friction is determined.

The formula for the effective coefficient of friction is,

μk=Iωir(Δt)n

• I is moment of inertia of the wheel.
• ωi is initial angular velocity of the wheel.
• r is radius of the wheel.
• Δt is time duration for the wheel to come rest

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