1. Assume the Earth to be a sphere of uniform density. Calculate: a. its moment of inertia b. its rotational kinetic energy c. Suppose that these energy could be harnessed for our use. For how long could the Earth supply 1.0 kW of power to each of the 7.8 x 10° persons on Earth? 2. A 25-kg child stands at a distance r=1.0m from the axis of a rotating merry-go-round. The merry-go-round can be approximated as a uniform solid disk with a mass of 500 kg and a radius of 2.0 m. Find the moment of inertia of this system.

1. Assume the Earth to be a sphere of uniform density. Calculate: a. its moment of inertia b. its rotational kinetic energy c. Suppose that these energy could be harnessed for our use. For how long could the Earth supply 1.0 kW of power to each of the 7.8 x 10° persons on Earth? 2. A 25-kg child stands at a distance r=1.0m from the axis of a rotating merry-go-round. The merry-go-round can be approximated as a uniform solid disk with a mass of 500 kg and a radius of 2.0 m. Find the moment of inertia of this system.

College Physics

1st Edition

ISBN:9781938168000

Author:Paul Peter Urone, Roger Hinrichs

Publisher:Paul Peter Urone, Roger Hinrichs

Chapter10: Rotational Motion And Angular Momentum

Section: Chapter Questions

Problem 26PE: While punting a football, a kicker rotates his leg about the hip joint. The moment of inertia of the...

See similar textbooks

Similar questions

A wheel is rotating about a fixed axis with constant angular acceleration 3 rad/s2. At different moments, its angular speed is 2 rad/s, 0. and +2 rad/s. For a point on the rim of the wheel, consider at these moments the magnitude of the tangential component of acceleration and the magnitude of the radial component of acceleration. Rank the following five items from largest to smallest: (a) |at| when = 2 rad/s, (b)|ar| when = 2 rad/s, (c)|ar| when = 0, (d) |at| when = 2 rad/s, and (e) |ar| when = 2 rad/s. If two items are equal, show them as equal in your ranking. If a quantity is equal to zero, show that fact in your ranking.
Integrated Concepts An ultracentrifuge accelerates from rest to 100,000 rpm in 2.00 min. (a) What is its angular acceleration in rad/s2? (b) What is the tangential acceleration of a point 9.50 cm from the axis of rotation? (c) What is the radial acceleration in m/s2 and multiples of g of this point at full rpm?
Suppose a child gets off a rotating merry-go-round, Does the angular velocity of the merry-go-round increase, decrease, or remain the same if: (a) He jumps off radially? (b) He Jumps backward to land motionless? (c) He jumps straight up and hangs onto an overhead tree branch? (d) He jumps off forward, tangential to the edge? Explain your answers. (Refer to Figure 10.34).
Everyday application: Suppose a yo-yo has a center shaft that has a 0.250 cm radius and that its string is being pulled. (a) If the string is stationary and the yo-yo accelerates away from it at a rate of 1.50 m/s2, what is the angular acceleration of the yo-yo? (b) What is the angular velocity after 0.750 s if it starts from rest? (c) The outside radius of the yo-yo is 3.50 cm. What is the tangential acceleration of a point on its edge?
A cylinder with moment of inertia I1 rotates with angular velocity 0 about a frictionless vertical axle. A second cylinder, with moment of inertia I2, initially not. rotating, drops onto the first cylinder (Fig. P8.73). Because the surfaces are rough, the two cylinders eventually reach the same angular speed . (a) Calculate . (b) Show that kinetic energy is lost in this situation, and calculate the ratio of the final lo the initial kinetic energy. Figure P8.73
Explain how you might use the apparatus described in Figure OQ10.7 to determine the moment of inertia of the wheel. Note: If the wheel does not have a uniform mass density, the moment of inertia is not necessarily equal to 12 MR2.
While exercising in a fitness center, a man lies face down on a bench and lifts a weight with one lower leg by contacting the muscles in the back of the upper leg. (a) Find the angular acceleration produced given the mass lifted is 10.0 kg at a distance of 28.0 cm from the knee joint, the moment of inertia of the lower leg is 0.900kg-m2 the muscle force is 1500 N, and its effective perpendicular lever arm is 3.00 cm. (b) How much work is done if the leg rotates through an angle of 20.0° with a constant force exerted by the muscle?
Consider the 12.0 kg motorcycle wheel shown in Figure 10.38. Assume it to be approximately an annular ring with an inner radius of 0.280 m and an outer radius of 0.330 m. The motorcycle is on its center stand, so that the wheel can spin freely. (a) If the drive chain exerts a force of 2200 N at a radius of 5.00 cm, what is the angular acceleration of the wheel? (b) What is the tangential acceleration of a point on the outer edge of the tire? (c) How long, starting from rest, does it take to reach an angular velocity of 80.0 rad/s? Figure 10.38 A motorcycle wheel has a moment of inertia approximately
A potters wheel moves uniformly from rest to an angular speed of 1.00 rev/s in 30.0 s. (a) Find its average angular acceleration in radians per second per second. (b) Would doubling the angular acceleration during the given period have doubled the final angular speed?
A baseball catcher extends his arm straight up to catch a fast ball with a speed of 40 m/s. The baseball is 0.145 kg and the catcher’s arm length is 0.5 m and mass 4.0 kg. (a) What is the angular velocity of the arm immediately after catching the ball as measured from the arm socket? (b) What is the torque applied if the catcher stops the rotation of his arm 0.3 s after catching the ball?
A top has moment of inertia 3.2104kgm2 and radius 4.0 cm from the center of mass to the pivot point. If it spins at 20.0 rev/s and is precessing, how many revolutions does it precess in 10.0 s?
A soccer player extends her lower leg in a kicking motion by exerting a force with the muscle above the knee in the front of her leg. She produces an angular acceleration of 30.00 rad/s2 and her lower leg has a moment of inertia of 0.750kg-m2 What is the force exerted by the muscle if its effective perpendicular lever arm is 1.90 cm?