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Chapter 8: 8-11MCQ (page 198)

A small mass m on a string is rotating without friction in a circle. The string is shortened by pulling it through the axis of rotation without any external torque, Fig. 8–39. What happens to the tangential velocity of the object?

(a) It increases.

(b) It decreases.

(c) It remains the same.

FIGURE 8-39

MisConceptual Questions 10 and 11.

Short Answer

Expert verified

The correct option is (a).

Step by step solution

01

Angular momentum

For angular momentum conservation, if the radius of the rotational path decreases, the moment of inertia decreases, and the rotational speed increases.Tangential speed is proportional to the angular speed; hence, the tangential speed increases.

The small mass is m.

02

Explanation

When you pull the string, the radius of the circular path decreases, and the moment of inertia of the mass also decreases. As there is no external torque, the angular momentum is conserved.

To maintain the conservation of the angular momentum of the mass, the angular velocity increases when the moment of inertia decreases.

Now, the tangential velocity of an object is proportional to the angular velocity. Therefore, the tangential velocity of that object also increases.

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Most popular questions from this chapter

The platter of the hard drive of a computer rotates at 7200 rpm (rpm = revolutions per minute = rev/min). (a) What is the angular velocity \(\left( {{{{\bf{rad}}} \mathord{\left/{\vphantom {{{\bf{rad}}} {\bf{s}}}} \right.} {\bf{s}}}} \right)\) of the platter? (b) If the reading head of the drive is located 3.00 cm from the rotation axis, what is the linear speed of the point on the platter just below it? (c) If a single bit requires \({\bf{0}}{\bf{.50}}\;{\bf{\mu m}}\) of length along the direction of motion, how many bits per second can the writing head write when it is 3.00 cm from the axis?

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