7. (a) A uniform solid disk of radius R and mass M is free to rotate on a frictionless pivot (solid dot) through a point on its rim. If the disk is released from rest from the position indicated in the figure, what is the linear speed of the center of mass when the disk reaches the position indicated by the dashed circle? Note that the center of the disk in the initial state is at the exact same height as the pivot. Hint: do not forget that the disk is rotating about a point on its rim. It is not rotating about its center. You will need to use the parallel axis theorem (see your textbook) to determine the correct moment of inertia. (b) What is the linear speed of the lowest point on the disk in the dashed position? (c) Repeat part (a) for a uniform hoop instead of a disk.R Problem 8. A smooth cube of mass m and edge length r slides with speed v on a horizontal surface with negligible friction. The cube then moves up a smooth incline that makes an angle with the horizontal. A solid cylinder of mass m and radius r rolls without slipping with its center of mass moving with speed v (so vcm = v) and encounters an incline with the same angle of inclination but with sufficient static friction that the cylinder continues to roll without slipping. (a) Which object will travel the greater distance up the incline and why? (b) Find the difference between the distances the objects travel up the incline. Problem 9. A spherical ball of mass m and radius r rolls without slipping do