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Q.46

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 332

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Short Answer

A V -diameter turntable rotates at on frictionless bearings. Two blocks fall from above, hit the turntable simultaneously at opposite ends of a diameter, and stick. What is the turntable's angular velocity, in rpm, just after this event?

Therefore, the final angular velocity of the turntable is .

See the step by step solution

Step by Step Solution

Step :1 Introduction 

According to conservation of angular momentum, the initial angular momentum of the object is equal to final angular momentum of the object.

Here, is the initial angular momentum of the object and is the final angular momentum of the object.

Step :2 Explanation

The initial angular momentum of the turntable

Here is the initial moment of inertia, is initial angular velocity. The final angular momentum of the turntable is,

Here, is the final moment of inertia and is final angular velocity.

Substitute in the equation and solve for .

The initial momentum of the inertia in turntable is

Here is mass of turntable and is radius of turntable.

The final angular momentum is due to turntable and two blocks. The final moment of inertia of the system is,

Here, is the mass of each block and is the distance of block from the center of the turntable.

Step  : 3 Relationship of radius and diameter 

The relation between radius and diameter on the turntable is

Here is the diameter of the turntable

Substitute for

Step :4 Substitution

Substitute in equation and solve

Substitute

=50rpm

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