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Q. 73

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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 thin, uniform rod of length L and mass M is placed vertically on a horizontal table. If tilted ever so slightly, the rod will fall over.
a. What is the speed of the center of mass just as the rod hits the table if there’s so much friction that the bottom tip of the rod does not slide? b. What is the speed of the center of mass just as the rod hits the table if the table is frictionless?

a) Speed of the center of mass just as the rod hits the table is

b) Speed of the center of mass just as the rod hits the for frictionless table is

See the step by step solution

Step by Step Solution

Part(a) Step1 : Given information

Length= L

Mass = M

Part(a) Step 2: Explanation

Moment of inertia of a rod is given by

Total energy , when rod is standing on table is

Kinetic energy of the rod when it hits the table

Substitute the value of inertia, we get

From the law of conservation of energy

Velocity is

Substitute in equation (4), we get

Part(b) Step 1 : Given information

Length= L

Mass = M

Part(b) Step2 : Explanation

Total energy of the standing rod is

( as center of mass is at middle of rod)

From the law of energy conservation

K=KE

As there is no friction so there will be no radial kinetic energy. so

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