85. A uniform cylinder of mass M and radius R is initially at rest on a rough horizontal surface. A light string is wrapped around the cylinder and is pulled straight up with a force T whose magnitude is 0.80 Mg. As a resuit, the cylinder slips and accelerates horizontally. The moment of inertia of the cylinder is I =MR2 and the coefficient of kinetic friction is 0.40. a 5:l0.4)Mg On the circle above, show all the forces applied on the cylinder. b. In terms of g, determine the linear acceleration, a of the center of the cylinder. Determine the angular acceleration, a of the cylinder. d. Explain the difference in results of linear acceleration a, and Ra. a. C. velocity elocity a

A proton is accelerated in a cyclotron to 5.0106m/s in 0.01 s. The proton follows a circular path. If the radius of the cyclotron is 0.5 km, (a) What is the angular momentum of the proton about the center at its maximum speed? (b) What is the torque on the proton about the center as it accelerates to maximum speed?

A particle has mass 0.5 kg and is traveling along the line x=5.0m at 2.0 m/s In the positive y-direction. What is the particle’s angular momentum about the origin?

A thin rod of length 2.65 m and mass 13.7 kg is rotated at anangular speed of 3.89 rad/s around an axis perpendicular to therod and through its center of mass. Find the magnitude of therods angular momentum.

A 0.2-kg particle is travelling along the line y=2.0m with a velocity 5.0 m/s. What is the angular momentum of the particle about the origin?

At a particular instant, a 1.0-kg particle’s position is , its velocity is , and the force on it is . (a) What is the angular momentum of the particle about the origin? (b) What is the torque on the particle about the origin? (c) What is the time rate of change of the particle’s angular momentum at this instant?

Jeff, running outside to play, pushes on a swinging door, causing its motion to be briefly described by = t2 + 0.800 t + 2.00,where t is in seconds and is in radians. At t = 0 and at t = 1.50s, what are the a. angular position, b. angular speed, and c. angularacceleration of the door?

A compact disc rotates at 500 rev/min. If the diameter of the disc is 120 mm, (a) what is the tangential speed of a point at the edge of the disc? (b) At a point halfway to the center of the disc?

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 gymnast does cartwheels along the floor and then launches herself into the air and executes several flips in a tuck while she is airborne. If her moment of inertia when executing the cartwheels is 13.5kgm2 and her spin rate is 0.5 rev/s, how many revolutions does she do in the air if her moment of inertia in the tuck is 3.4kgm2 and she has 2.0 s to do the flips in the air?