Consider a solid cylinder of mass m and radius r and a solid sphere of mass M and radius R are placed at rest on the top of an inclined plane that makes an angle 0 with the ground. The length of the inclined plane is L. Now solve the following problems. (a) Find the moment of inertia of the cylinder and sphere. (b) Find the potential energy of the cylinder and the sphere when they are at the top of the inclined plane. (c) Now we let go of the cylinder and the sphere at the same time so that the roll without slipping along the incline plane. Find out which one of the solid bodies have greater linear velocity than the other when they come down from the inclined plane.

Consider a solid cylinder of mass m and radius r and a solid sphere of mass M and radius R are placed at rest on the top of an inclined plane that makes an angle 0 with the ground. The length of the inclined plane is L. Now solve the following problems. (a) Find the moment of inertia of the cylinder and sphere. (b) Find the potential energy of the cylinder and the sphere when they are at the top of the inclined plane. (c) Now we let go of the cylinder and the sphere at the same time so that the roll without slipping along the incline plane. Find out which one of the solid bodies have greater linear velocity than the other when they come down from the inclined plane.

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter10: Rotational Motion

Section: Chapter Questions

Problem 44P: Consider two objects with m1 m2 connected by a light string that passes over a pulley having a...

See similar textbooks

Similar questions

The mass of a hoop of radius 1.0 m is 6.0 kg. It rolls across a horizontal surface with a speed of 10.0 m/s. (a) How much work is required to stop the hoop? (b) If the hoop starts up a surface at 30 to the horizontal with a speed of 10.0 m/s, how far along the incline will it travel before stopping and rolling back down?
Show that when A+B=C then A2+B2+2ABcos , where is the angle between vectors A and B .
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.
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 screwdriver turns a screw an angle of 5.85 radians by applying a torque given by (in Nm) 02 T=2.12 + 6. Calculate the work done, W by the torque. Enter W, measured in Joules, correct to three significant figures:
A solid uniform sphere of radius .250 m and mass 45.0 kg rolls down a ramp of length 4.50 m that makes an angle of 14 degrees with the horizontal. The sphere starts from rest from the top of the ramp. Find the speed of the sphere when it reaches the bottom of the ramp.
A hollow cylinder with mass M = 3 kg and radius R = 0.6 m rolls down a 4 m high hill. What would be the speed ofthe cylinder when it reaches the bottom of the hill?
a rigid assembly of a thin hoop (of mass mand radius R = 0.150 m) and a thin radial rod (of mass m and length L = 2.00R). The assembly is upright, but if we give it a slight nudge, it will rotate around a horizontal axis in the plane of the rod and hoop, through the lower end of the rod. Assuming that the energy given to the assembly in such a nudge is negligible, what would be the assembly’s angular speed about the rotation axis when it passes through the upside-down (inverted) orientation?
A 5 kg cylinder 0.5 m in diameter rolls down a plane 5 m long inclined 30° with the horizontal at the bottom of the incline. What is its (a) total kinetic energy, (b) linear speed, (c) angular speed, (d) rotational kinetic energy, and (e) translational kinetic energy? Neglect friction.
In Fig. below, two blocks, of masses 2 kg and 3 kg, are connected by a light string that passes over a pulley of moment of inertia 0.004 kg · m2 and radius 5 cm. The coefficient of friction for the table top is 0.30. The blocks are released from rest. Using energy methods, one can deduce that after the upper block has moved 0.6 m, its speed is:
A solid sphere of uniform density (weight = 1.8 lbs starts from rest and rolls down a ramp (H = 1.31 m, θθ = 28.5°.)Find the speed of the sphere's CM when it reaches the bottom of the ramp.
A horizontal 800-N merry-go-round is a solid disk of radius 1.50 m and is started from rest by aconstant horizontal force of 50.0 N applied tangentially to the edge of the disk. Find the kinetic energyof the disk after 3.00 s.