A yoyo is a toy made of three uniform density disks with a string wrapped around the middle disk. The middle disk has a mass and radius ; the outer disks each have mass and radius . The string has negligible mass and stretches a negligible amount. Analyze the following situation. As the yoyo is moving downward, you pull up with a constant force F and as you pull, your hand moves upward a distance . At the beginning of your move the yoyo was headed downward with speed and angular speed . When your hand has moved up a distance , the yoyo has moved down a smaller distance and has speed downward and angular speed . Assume that the string doesn't slip or rub against the outer disks, so there is no change in temperature of the yoyo. Required:
a. The moment of inertia of the yoyo is the sum of the moments of inertia of the three disks about the axis of rotation. Calculate this quantity.
b. Calculate the speed ð£2.
c. Calculate the angular speed ð2.