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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鈥�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

An oxygen molecule consists of two oxygen atoms whose total mass is \({\bf{5}}{\bf{.3 \times 1}}{{\bf{0}}^{{\bf{ - 26}}}}\;{\bf{kg}}\) and the moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is \({\bf{1}}{\bf{.9 \times 1}}{{\bf{0}}^{{\bf{ - 46}}}}\;{\bf{kg}} \cdot {{\bf{m}}^{\bf{2}}}\). From these data, estimate the effective distance between the atoms.

Question:(II) A ball of radius rrolls on the inside of a track of radius R(see Fig. 8鈥�53). If the ball starts from rest at the vertical edge of the track, what will be its speed when it reaches the lowest point of the track, rolling without slipping?

In what direction is the Earth鈥檚 angular velocity vector as it rotates daily about its axis, north or south?

Two wheels having the same radius and mass rotate at the same angular velocity (Fig. 8鈥�38). One wheel is made with spokes so nearly all the mass is at the rim. The other is a solid disk. How do their rotational kinetic energies compare?

(a) They are nearly the same.

(b) The wheel with spokes has about twice the KE.

(c) The wheel with spokes has higher KE, but not twice as high.

(d) The solid wheel has about twice the KE.

(e) The solid wheel has higher KE, but not twice as high.

FIGURE 8-38

MisConceptual Question 7.

A uniform rod of mass M and length l can pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8鈥�63. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8鈥�20g.]
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