A 23 mm diameter glass marble with a mass of 15 g rolls without slipping down a track toward a vertical loop of radius R = 13 cm, as shown in the figure. Approximate the minimum translational speed umin the marble must have in order to complete the loop without falling off the track when it is a height H = 25 cm above the bottom of the loop.

A 23 mm diameter glass marble with a mass of 15 g rolls without slipping down a track toward a vertical loop of radius R = 13 cm, as shown in the figure. Approximate the minimum translational speed umin the marble must have in order to complete the loop without falling off the track when it is a height H = 25 cm above the bottom of the loop.

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter11: Angular Momentum

Section: Chapter Questions

Problem 50P: A roller coaster has mass 3000.0 kg and needs to make it safely through a vertical circular loop of...

See similar textbooks

Similar questions

A boy rides his bicycle 2.00 km. The wheels have radius 30.0 cm. What is the total angle the tires rotate through during his trip?
The precession angular velocity of a gyroscope is 1.0 rad/s. If the mass of the rotating disk is 0.4 kg and its radius is 30 cm, as well as the distance from the center of mass to the pivot, what is the rotation rate in rev/s of the disk?
Consider two objects with m1 m2 connected by a light string that passes over a pulley having a moment of inertia of I about its axis of rotation as shown in Figure P10.44. The string does not slip on the pulley or stretch. The pulley turns without friction. The two objects are released from rest separated by a vertical distance 2h. (a) Use the principle of conservation of energy to find the translational speeds of the objects as they pass each other. (b) Find the angular speed of the pulley at this time.
A gyroscope has a 0.5-kg disk that spins at 40 rev/s. The center of mass of the disk is 10 cm from a pivot which is also the radius of the disk. What is the precession angular velocity?
A cylinder with rotational inertia I1=2.0kgm2 rotates clockwise about a vertical axis through its center with angular speed 1=5.0rad/s . A second cylinder with rotational inertia I2=1.0kgm2 rotates counterclockwise about the same axis with angular speed 2=8.0rad/s . If the cylinders couple so they have the same rotational axis what is the angular speed of the combination? What percentage of the original kinetic energy is lost to friction?
A diver off the high board imparts an initial rotation with his body fully extended before going into a tuck and executing three back somersaults before hitting the water. If his moment of inertia before the tuck is 16.9kgm2 and after the tuck during the somersaults is 4.2kgm2 , what rotation rate must he impart to his body directly off the board and before the tuck if he takes 1.4 s to execute the somersaults before hitting the water?
A particle travels at a uniform linear speed around a circle of radius r = 0.5 m, completing one revolution in 12 s. a. What is the value of the linear speed v? b. Find the particles angular speed. c. What are the angle and arc length s swept out by the particle in 4 s?
An electric food processor comes with many attachments forblending and slicing food. Assume the motor maintains thesame angular speed for all the various attachments. The largestattachment has a diameter of 12.0 cm, and the smallest has a diameter of 5.00 cm. Find the ratio of the translational speeds of points on the edges of each attachment.
A solid cylinder of radius 10.0 cm rolls down an incline with slipping. The angle of the incline is 30 . The coefficient of kinetic friction on the surface is 0.400. What is the angular acceleration of the solid cylinder? What is the linear acceleration?
An electric sander consisting of a rotating disk of mass 0.7 kg and radius 10 cm rotates at 15 rev/sec. When applied to a rough wooden wall the rotation rate decreases by 20 . (a) What is the final rotational kinetic energy of the rotating disk? (a) How much has its rotational kinetic energy decreased?
A massless tether with a masses tied to both ends rotates about a fixed axis through the center. Can the total acceleration of the tether mass combination be zero If the angular velocity Is constant?
What is (a) the angular speed and (b) the linear speed of a point on Earth’s surface at latitude 30N . Take the radius of the Earth to be 6309 km. (c) At what latitude would your linear speed be 10 m/s?