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Q. 71

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 334

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Short Answer

A cylinder of radius R, length L, and mass M is released from rest on a slope inclined at angle θ. It is oriented to roll straight down the slope. If the slope were frictionless, the cylinder would slide down the slope without rotating. What minimum coefficient of static
friction is needed for the cylinder to roll down without slipping?

Coefficient of friction is

See the step by step solution

Step by Step Solution

Step1: Given Information

A cylinder of radius= R,

length = L, and

mass = M is released from rest on a slope

angle of inclination= θ

Step2: Explanation

Lets first draw the free body diagram as below

Equate horizontal and vertical force

As net force in perpendicular direction is zero so

N = mg cosθ ............................(1)

and

mg sinθ - fs = ma ........................(2)

Where fs is frictional force

Find the torque acting on cylinder.

As mass passes through axis of center so only frictional force will cause the torque

Torque is also expressed as

Substitute

Upon simplification

Now substitute the value of fs in equation (1)

We know frictional force is

So

Substitute the value from equation(1) and (3)

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