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Chapter 9: Q13 P (page 377)
If an object has a moment of inertia and rotates with an angular speed of , what is its rotational kinetic energy?
The rotational kinetic energy is
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A sphere of uniform density with mass 22 kg and radius 0.7 m is spinning, making one complete revolution every 0.5 s. The center of mass of the sphere has a speed of4 m?s(a) What is the rotational kinetic energy Of the sphere? (b) What is the total kinetic energy of the sphere?
A string is wrapped around a uniform disk of mass M and radius R. Attached to the disk are four low-mass rods of radius b, each with a small mass m at the end (Figure 9.63).
The apparatus is initially at rest on a nearly frictionless surface. Then you pull the string with a constant force F. At the instant when the center of the disk has moved a distance d, an additional length w of string has unwound off the disk. (a) At this instant, what is the speed of the center of the apparatus? Explain your approach. (b) At this instant, what is the angular speed of the apparatus? Explain your approach.
Consider the acceleration of a car on dry pavement, if there is no slipping. The axle moves at speed v, and the outside of the tire moves at a speed relative to the axle. The instantaneous velocity of the bottom of the tire is zero. How much work is done by the force exerted on the tire by the road? What is the source of the energy that increases the car鈥檚 translational kinetic energy?
You hang by your hands from a tree limb that is a heightabove the ground, with your center of mass a heightabove the ground and your feet a heightabove the ground, as shown in Figure 9.56. You then let yourself fall. You absorb the shock by bending your knees, ending up momentarily at rest in a crouched position with your center of mass a heightabove the ground. Your mass is M. You will need to draw labeled physics diagrams for the various stages in the process.
(a) What is the net internal energy change in your body (chemical plus thermal)? (b) What is your speed vat the instant your feet first touch the ground? (c) What is the approximate average force Fexerted by the ground on your feet when your knees are bending? (d) How much work is done by this force,F?
A uniform-density sphere whose mass is and radius is makes one complete rotation every. What is the rotational kinetic energy of the sphere?
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