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Chapter 11: Q84P (page 416)

A bicycle wheel with a heavy rim is mounted on a lightweight axle, and one end of the axle rests on top of a post. The wheel is observed to presses in the horizontal plane. With the spin direction shown in figure11.111, does the wheel process clockwise or counter wise? Explain in detail, including appropriate diagrams.

Short Answer

Expert verified

The torque points into the page and then the wheel process in clockwise direction.

Step by step solution

01

Definition of torque

Torque is defined as the force which causes the rotation of the object about an axis.

02

Find the torque point of the wheel

The direction of bicycle wheel rotation is as shown in the following figure.

The bicycle wheel on the axle behaves like a gyroscope with one of the axle on the vertical support. The wheel rotates in clockwise direction around its own axis with spin angular speed蝇 . The rotational angular momentumLrot鈫�of the wheel points horizontally but it is changing as the gyroscope processes. The forces that are acting on the system are force exerts by support and mass, at the center of the spinning wheel.

The translational angular momentum remains constant whereas the rotational angular momentum is change asdL鈫�dt .

Thus, the torque points into the page and then the wheel process in clockwise direction.

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Most popular questions from this chapter

A rotating uniform-density disk of radius 0.6mis mounted in the vertical plane, as shown in Figure 11.88.The axle is held up by supports that are not shown, and the disk is free to rotate on the nearly frictionless axle. The disk has mass 5kg.A lump of clay with mass0.4kgfalls and sticks to the outer edge of the wheel at the location 鉄�-0.36,0.480,0鉄�m,relative to an origin at the centre of the axle. Just before the impact the clay has speed 8m/s,and the disk is rotating clockwise with angular speed0.51radians/s.

(a) Just before the impact, what is the angular momentum (magnitude and direction) of the combined system of wheel plus clay about the centerC?(As usual,xis to the right,yis up, andzis out of the screen, toward you.) (b) Just after the impact, what is the angular momentum (magnitude and direction) of the combined system of wheel plus clay about the centerC?(c) Just after the impact, what is the angular velocity (magnitude and direction) of the wheel? (d) Qualitatively, what happens to the linear momentum of the combined system? Why? (A) There is no change because linear momentum is always conserved. (B) Some of the linear momentum is changed into angular momentum. (C) Some of the linear momentum is changed into energy. (D) The downward linear momentum decreases because the axle exerts an upward force.

Because the Earth is nearly perfectly spherical, gravitational forces act on it effectively through its center. Explain why the Earth鈥檚 axis points at the North star all year long. Also explain why the earth鈥檚 rotation speed stays the same throughout the year (one rotation per 24h). In your analysis, does it matter that the Earth is going around the sun?

In actual fact, the Earth is not perfectly spherical. It bulges out a bit at the equator, and tides tend to pile up water at one side of the ocean. As a result, there are small torque exerted on the Earth by other bodies, mainly the sun and the moon. Over many thousands of years there are changes in what portion of sky the Earth鈥檚 axis points towards (Change of direction of rotational angular momentum), and changes in the length of a day (change of magnitude of rotational angular momentum).

In Figure 11.96a spherical non-spinning asteroid of mass\(M\)and radius\(R\)moving with speed\({v_1}\)to the right collides with a similar non-spinning asteroid moving with speed\({v_2}\)to the left, and they stick together. The impact parameter is\(d\).Note that\({I_{sphere}} = \frac{2}{5}M{R^2}.\)

After the collision, what is the velocity \({v_{CM}}\) of the center of mass and the angular velocity \(\omega \) about the center of mass? (Note that each asteroid rotates about its own center with this same \(\omega \)).

A uniform-density wheel of mass and radius rotates on a low-friction axle. Starting from rest, a string wrapped around the edge exerts a constant force of 15Nfor0.6s (a) what is the final angular speed? (b) what is the average angular speed? (c) Through how big an angle did the wheel turn? (d) How much string come off the wheel?

At a particular instant the location of an object relative to location \(A\) is given by the vector \({\overrightarrow r _A} = \left\langle {6,6,0} \right\rangle {\rm{m}}\). At this instant the momentum of the object is \(\overrightarrow p = \left\langle { - 11,13,0} \right\rangle {\rm{kg}} \cdot {\rm{m}}/{\rm{s}}.\) What is the angular momentum of the object about location \(A\)?
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