•• P28 A string is wrapped around a disk of mass 2.1 kg (its density is not necessarily uniform). Starting from rest, you pull the string with a constant force of 9 N along a nearly frictionless surface. At the instant when the center of the disk has moved a distance 0.11 m, your hand has moved a distance of 0.28 m (Figure 9.51). 2.1 kg 9N 0.11 m 9N 0.28 m Figure 9.51 (a) At this instant, what is the speed of the center of mass of the disk? (b) At this instant, how much rotational kinetic energy does the disk have relative to its center of mass? (c) At this instant, the angular speed of the disk is 7.5 rad/s. What is the moment of inertia of the disk?

•• P28 A string is wrapped around a disk of mass 2.1 kg (its density is not necessarily uniform). Starting from rest, you pull the string with a constant force of 9 N along a nearly frictionless surface. At the instant when the center of the disk has moved a distance 0.11 m, your hand has moved a distance of 0.28 m (Figure 9.51). 2.1 kg 9N 0.11 m 9N 0.28 m Figure 9.51 (a) At this instant, what is the speed of the center of mass of the disk? (b) At this instant, how much rotational kinetic energy does the disk have relative to its center of mass? (c) At this instant, the angular speed of the disk is 7.5 rad/s. What is the moment of inertia of the disk?

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter13: Rotation Ii: A Conservation Approach

Section: Chapter Questions

Problem 66PQ: To give a pet hamster exercise, some people put the hamster in a ventilated ball andallow it roam...

See similar textbooks

Similar questions

A massless spring of constant k = 78.4 N/m is fixed on the left side of a level track. A block of mass m = 0.50 kg is pressed against the spring and compresses it a distance d, as in Figure P7.74. The block (initially at rest) is then released and travels toward a circular loop-the-loop of radius R = 1.5 m. The entire track and the loop-the-loop are frictionless, except for the section of track between points A and B. Given that the coefficient of kinetic friction between the block and the track along AB is k = 0.30 and that the length of AB is 2.5 m, determine the minimum compression d of the spring that enables the block to just make it through the loop-the-loop at point C. Hint: The force exerted by the track on the block will be zero if the block barely makes it through the loop-the-loop. Figure P7.74
In bicycling for aerobic exercise, a woman wants her heart rate to be between 136 and 166 beats per minute. Assume that her heart rate is directly proportional to her mechanical power output within the range relevant here. Ignore all forces on the woman-bicycle system except for static friction forward on the drive wheel of the bicycle and an air resistance force proportional to the square of her speed. When her speed is 22.0 km/h, her heart rate is 90.0 beats per minute. In what range should her speed be so that her heart rate will be in the range she wants?
An open box slides across a frictionless, icy surface of a frozen lake. What happens to the speed of the box as water from a rain shower falls vertically downward into the box? Explain.
Two identical particles, each of mass 1 000 kg, are coasting in free space along the same path, one in front of the other by 20.0 m. At the instant their separation distance has this value, each particle has precisely the same velocity of 800 m/s. What are their precise velocities when they are 2.00 m apart? Figure P13 74
A particle is suspended from a post on top of a can by a light string of length L. as shown in Figure P9.57a. The can and particle are initially moving to the right at constant speed the with the string vertical. The can suddenly comes to rest when it runs into and sticks to a bumper as shown in Figure P9.57b. The suspended panicle swings through an angle . (a) Show that the original speed of the cart can be computed from. vi=2gL(1cos) (b) If the bumper is still exerting a horizontal force on the cart when the hanging panicle is at its maximum angle forward from the vertical. at what moment does the bumper stop exerting a horizontal force?
The system shown in Figure P5.49 has an acceleration of magnitude 1.50 m/s2. Assume that the coefficient of kinetic friction between block and incline is the same for both inclines. Find (a) the coefficient of kinetic friction and (b) the tension in the string.
When there is a global heating trend on Earth, the atmosphere expands and the length of the day increases very slightly. Explain why the length of a day increases.
A giant swing at an amusement park consists of a 365-kg uniform arm 10.0 m long, with two seats of negligible mass connected at the lower end of the arm (Fig. P8.53). (a) How far from the upper end is the center of mass of the arm? (b) The gravitational potential energy of the arm is the same as if all its mass were concentrated at the center of mass. If the arm is raised through a 45.0 angle, find the gravitational potential energy, where the zero level is taken to be 10.0 m below the axis, (c) The arm drops from rest from the position described in part (b). Find the gravitational potential energy of the system when it reaches the vertical orientation. (d) Find the speed of the seats at the bottom of the swing.
Io and Europa are two of Jupiters many moons. The mean distance of Europa from Jupiter is about twice as far as that for Io and Jupiter. By what factor is the period of Europas orbit longer than that of Ios?
Why is the following situation impossible? In a new casino, a supersized pinball machine is introduced. Casino advertising boasts that a professional basketball player can lie on top of the machine and his head and feet will not hang off the edge! The hall launcher in the machine sends metal halls up one side of the machine and then into play. The spring in the launcher (Fig. P7.44) has a force constant of 1.20 N/cm. The surface on which the ball moves is inclined = 10.0 with respect to the horizontal. The spring is initially compressed its maximum distance d = 5.00 cm. A ball of mass 100 g is projected into play by releasing the plunger. Casino visitors find the play of the giant machine quite exciting. Figure P7.44
A 6 000-kg freight car rolls along rails with negligible friction. The car is brought to rest by a combination of two coiled springs as illustrated in Figure P6.27 (page 188). Both springs are described by Hookes law and have spring constants k1 = 1 600 N/m and k2, = 3 400 N/m. After the first spring compresses a distance of 30.0 cm, the second spring acts with the first to increase the force as additional compression occurs as shown in the graph. The car comes to rest 50.0 cm after first contacting the two-spring system. Find the cars initial speed.
George of the Jungle, will mass m, swings on a light vine hanging from a stationary tree branch. A second vine of equal length hangs from the same point, and a gorilla of larger mass M swings in the opposite direction on it. Both vines are horizontal when the primates start from rest at the same moment. George and the gorilla meet at the lowest point of their swings. Each is afraid that one vine will break, so they grab each other and hang on. They swing upward together, reaching a point where the vines make an angle of 35.0 with the vertical. Find the value of the ratio at m/M.