A thin-walled, hollow spherical shell of mass m and radius r starts from rest and rolls without slipping down the track shown in the figure (Figure Points A and B are on a circular part of the track having radius R. The diameter of the shell is very small compared to họ and R, and the work done by the rolling friction is negligible. What is the height ho for which this shell will make a complete loop-the-loop on the circular part of the track, with a velocity át the top that is 3 times the minimum, velocity necessary to complete the loop without loosing contact with the loop. express as a constant multiplied by R. For a thin spherical shell, I-(2/3)Mr2 Sgile Shell ho B

A thin-walled, hollow spherical shell of mass m and radius r starts from rest and rolls without slipping down the track shown in the figure (Figure Points A and B are on a circular part of the track having radius R. The diameter of the shell is very small compared to họ and R, and the work done by the rolling friction is negligible. What is the height ho for which this shell will make a complete loop-the-loop on the circular part of the track, with a velocity át the top that is 3 times the minimum, velocity necessary to complete the loop without loosing contact with the loop. express as a constant multiplied by R. For a thin spherical shell, I-(2/3)Mr2 Sgile Shell ho B

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter12: Rotation I: Kinematics And Dynamics

Section: Chapter Questions

Problem 60PQ

See similar textbooks

Similar questions

A roller coaster has mass 3000.0 kg and needs to make it safely through a vertical circular loop of radius 50.0 m. What is the minimum angular momentum of the coaster at the boom of the loop to make it safely through? Neglect friction on the track. Take the coaster to be a point particle.
If you know the velocity of a particle, can you say anything about the particle’s angular momentum?
A 40.0-kg solid cylinder is rolling across a horizontal surface at a speed of 6.0 m/s. How much work is required to stop it?
A hollow cylinder that is rolling without slipping is given a velocity of 5.0 m/s and rolls up an incline to a vertical height of 1.0 m. If a hollow sphere of the same mass and radius is given the same initial velocity how high vertically does it roll up the incline?
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?
Consider two cylinders that start down identical inclines from rest except that one is frictionless. Thus one cylinder rolls without slipping, while the other slides frictionlessly without rolling. They both travel a sh01t distance at the bottom and then start up another incline. (a) Show that they both reach the same height on the other incline, and that this height is equal to their original height. (b) Find the ratio of the time the rolling cylinder takes to reach the height on the second incline to the time the sliding cylinder takes to reach the height on the second incline. (c) Explain why the time for the rolling motion is greater than that for the sliding motion.
Two spheres, one hollow and one solid, are rotating with the same angular speed around an axis through their centers. Both spheres have the same mass and radius. Which sphere, if either, has the higher rotational kinetic energy? (a) The hollow I sphere, (b) The solid sphere, (c) They have the same kinetic energy.
Two particles of equal mass travel with the same speed in opposite directions along parallel lines separated by a distance d Show that the angular momentum of this two- particle system is the same no matter what point is used as the reference for calculating the angular momentum.
Which of the entries in Table 10.2 applies to finding the moment of inertia (a) of a long, straight sewer pipe rotating about its axis of symmetry? (b) Of an embroidery hoop rotating about an axis through its center and perpendicular to its plane? (c) Of a uniform door turning on its hinges? (d) Of a coin turning about an axis through its center and perpendicular to its faces?
A rigid body with a cylindrical cross-section is released from the top of a 30 incline. It rolls 10.0 m to the bottom in 2.60 s. Find the moment of inertia of the body In terms of its mass m and radius r.
A digital audio compact disc carries data, each bit of which occupies 0.6 m along a continuous spiral track from the inner circumference of the disc to the outside edge. A CD player turns the disc to carry the track counterclockwise above a lens at a constant speed of 1.30 m/s. Find the required angular speed (a) at the beginning of the recording, where the spiral has a radius of 2.30 cm, and (b) at the end of the recording, where the spiral has a radius of 5.80 cm. (c) A full-length recording lasts for 74 min 33 s. Find the average angular acceleration of the disc. (d) Assuming that the acceleration is constant, find the total angular displacement of the disc as it plays. (e) Find the total length of the track.
Which rolls down an inclined plane faster, a hollow cylinder or a solid sphere? Both have the same mass and radius.