- A uniform solid sphere is released from rest at the top of a 2.5 m long board that is inclined at22° above the horizontal. The mass of the sphere is 25 kg and the radius is 12 cm, (a) what isthe moment of inertia of the sphere? Then neglecting energy losses calculate the followingvalues once the sphere has reached the bottom of the incline assuming that it rolls withoutslipping: (b) the translational speed of the center of mass, and (c) the angular speed of thesphere about its center of mass. Include a relevant diagram of the situation. [Diagram 2 pts.]

Please refer the images for detailed answer,Reference: Fundamentals of Physics by David Halliday,…

Answered: - A uniform solid sphere is released…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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A uniform cylinder of radius 10 cm and mass 20 kg is mounted so as to rotate freely about a horizontal axis that is parallel to and 5.0 cm from the central longitudinal axis of the cylinder. (a) What is the rotational inertia of the cylinder about the axis of rotation? (b) If the cylinder is released from rest with its central longitudinal axis at the same height as the axis about which the cylinder rotates, what is the angular speed of the cylinder as it passes through its lowest position?
A uniform solid sphere with the radius R=20 cm and a uniform cylinder, with the radius R1=10 cm is placed side by side at the top of an incline of height 150 cm. If they are released from rest at the same time and roll without slipping (friction force is zero). Calculate their speeds when they reach the bottom of incline.
Calculate moment of inertia of a desk with a mass of 6.00 kg and a radius of 0.250 m, with a axis of rotational half way between its center and it’s rim.
In the figure, a constant horizontal force F→app of magnitude 31.0 N is applied to a uniform solid cylinder by fishing line wrapped around the cylinder. The mass of the cylinder is 17.5 kg, its radius is 0.656 m, and the cylinder rolls smoothly on the horizontal surface. (a) What is the magnitude of the acceleration of the center of mass of the cylinder? (b) What is the magnitude of the angular acceleration of the cylinder about the center of mass? (c) In unit-vector notation, what is the frictional force acting on the cylinder?
The spool has a mass of 30 kg and a radius of gyration of ko= 0.4 m, and r is 0.3 m. Neglect the mass of the cord. If the 10-kg block A is released from rest, determine the distance the block must fall in order for the spool to attain an angular velocity - 10 rad/s and the cord force during the motion. OF
In a compact disc (CD) player, as the read head moves out from the center of the disc, the angular speed of the disc changes so that the linear speed at the position of the head remains at a constant value of about 1.2 m/s. (a) Find the angular speed of a CD of radius 6.45 cm when the read head is at r = 2.2 cm and again at r = 5.8 cm. (b) An old-fashioned record player rotates at a constant angular speed, so the linear speed of the record groove moving under the detector (the stylus) changes. Find the linear speed of a 45.0-rpm record at points 2.3 cm and 5.9 cm from the center. (c) In both the CDs and phonograph records, information is recorded in a continuous spiral track. Calculate the total length of the track for a CD designed to play for 1 hour and 15 minutes.
A uniform solid sphere of mass 12.0 kg and radius 7.0 cm rotates at 300 revolutions per minute (rpm) on an axis passing through its center. Calculate: a) Its moment of inertia b) Its rotational kinetic energy c) The angular momentum (L), that is, the magnitude of the product Iw, in the appropriate IS units d) Based on the general definition of the moment of inertia (I = Mr²), determine the radius of gyration of the sphere around the axis that passes through its center.
A pulley on a frictionless axle has the shape of a uniform solid disk of mass 2.50 kg and radius 0.150m. A 1.50 kg stone is attached to a very light wire that is wrapped around the rim of the pulley (Fig), and the system isreleased from rest. (a) How far must the stone fall so that the stone has 1.20 m/s speed? (b) What percentage of the total kinetic energy does the pulley have?
(a) What is the maximum angular velocity of the arm if the muscle is attached 1 cm from the elbow? (b) What is the macimum weight that can be held in the hand if the muscle is attached 1 cm from the elbow? (c) What is the maximum angular velocity of the arm if the muscle is attached 3 cm from the elbow? (d) What is the maximum weight that can be held if the muscle is attached 3 cm from the elbow?

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