- 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 solid, uniform disk of radius 0.250 m and mass 55.0 kg rollsdown a ramp of length 4.50 m that makes an angle of 15.0°with the horizontal. The disk starts from rest from the top ofthe ramp. Find (a) the speed of the disk’s center of mass whenit reaches the bottom of the ramp and (b) the angular speedof the disk at the bottom of the ramp.
a) A diver leaps from a platform and immediately goes into a tuck position. If we assume that the diver has an initial angular velocity of 7.5 rad/sec, and has an angular acceleration of -0.22rad/sec2,how long will it take for the diver to complete 2 full revolutions?b) Assume that the diver is 6 m above the water with an initial vertical velocity of 1.74 m/s when she begins to rotate. Will she be able to complete 2 full revolutions before hitting the water? Why or why not?
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
2) A uniform disk with mass 40.0 kg and radius 0.200 m is pivoted at its center about a horizontal, frictionless axle that is stationary. The disk is initially at rest, and then a constant force F = 30.0 N is applied tangent to the rim of the disk. (a) What is the magnitude of the tangential velocity of a point on the rim of the disk after the disk has turned through 0.200 revolution? (b) What is the magnitude of the resultant acceleration of a point on the rim of the disk after the disk has turned through 0.200 revolution?
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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