A primitive yo-yo has a massless string wrapped around a solid cylinder with mass M and radius R. You hold the free end of the string stationary and release the cylinder from rest. The string unwinds but does not slip or stretch as the cylinder descends and rotates. Using energy considerations, find the speed Vem of the cylinder's center of mass after it has descended a distance h. (gh)

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 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 top has moment of inertia 3.2104kgm2 and radius 4.0 cm from the center of mass to the pivot point. If it spins at 20.0 rev/s and is precessing, how many revolutions does it precess in 10.0 s?

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 potter’s disk spins from rest up to 10 rev/s in 15 s. The disk has a mass 3.0 kg and radius 30.0 cm. What is the angular momentum of the disk at t=5s , t=10s ?

A stick with a mass of 0.164 kg and a length of 1.00 mis pivoted about one end so it can rotate without friction about a horizontal axis. The meter stick is held in a horizontal position and released.    Part AAs it swings through the vertical, calculatethe change in gravitational potential energy that has occurred.Use 9.81 m/s2for the acceleration due to gravity. Part BAs it swings through the vertical, calculate the angular speed of the stick.    Part CAs it swings through the vertical, calculate the linear speed of the end of the stick opposite the axis.     Part DFind the ratio of the speed of a particle that has fallen a distance of 1.00 m, starting from rest, to the speed from part (C).

While spinning down from 500.0 rpm to rest, a solid uniform disk does 51 KJ of work. If the radius of the disk is r=400mm what is it's mass?.

A point mass m = 3 kg can move on a straight track from point A to point B. The points are on the parameter of a circular table of radius R = 8.8 m which is rotating around its center counterclockwise at constant angular velocity w = 3 rad/s. ŷR B R R At t = () the mass is at point A and begins to move at constant speed vo = 2 m/s to point B. Note that the speed remains constant during the process. What is the Coriolis force on the mass during its motion from point A to point B? a. 25.46*(Xr+Yr) O b. 50.91*(-Xr-Yr) O c. 36.00*(Xr-Yr) O d. 9.00*(-Xr+Yr) O e. 12.73*(Xr+Yr) Of. 36.00*(Xr+Yr) O g. 36.00*(-Xr+Yr) Oh. 25.46*(Xr-Yr)

A ball of mass 2.3 kg, at one end of a string of length L=4.5 m, rotates in a vertical circle just fast enough to prevent the string from going slack at the top of the circle. Assuming mechanical energy is conserved, the speed of the ball (in m/s) at the bottom of the circle is: m a. 10.50 Ob. 8.13 Oc. 9.39 Od. 14.85 Oe. 6.64