39. 40. 4]. The blades of a circular fan running at low speed turn at 250 rpm. When the fan is switched to high speed' the rotation rate increases to 350 rpm. This change ofthe rotation rate occurs uniformly and takes 5.?5 seconds. Remember to convert rpm to radfs. a. What is the angular acceleration (a) needed to go from low to high spccd? b. How many rotations do the fan blades go through while the fan is accelerating? c. If the moment of inertia of the fan blades is 0.23 kg m2, what is the torque provided by the motor on the fan blades? A top spins and slows down at an angular acceleration of -l.5 radiansisec2 until it topples. 1f the top will topple at an angular speed of 150 radians per second or less, and the top toppled after spinning for 45 seconds, what was the initial angular velocity ofthc top? A solid disk of unknown mass and known radius R is used as a pulleyr in a lab experiment, as shown. A small block of mass m is attached to a string, the other end of which is attached to the pulley and wrapped around it several times. The block of mass m is released from rest and takes a time tto fall the distance D to the floor. a. Write an equation that can be used to calculate the Einear acceleration a of the falling block in terms of the given quantities. TIE] b. The time t is measured for various heights D and the data are recorded in the following table. ii What quantities should be graphed in order to best determine the acceleration of the block? Explain your reasoning. {continued from previous page] ii. 0n the grid below, plot the quantities determined in (b) i., label the axes, and draw the best-t line to the data. 5 i. 23* {41\" as- 4.;a. . .'J'. 1 . P iii.Use your graph to calculate the magnitude of the acceleration c. Calculate the rotational inertia of the pulley in terms of m, R, a, and fundamental constants. d. The value of acceleration found in (b)iii, along with numerical values for the given quantities and your answer to (c), can be used to determine the rotational inertia of the pulley. The pulley is removed from its support and its rotational inertia is found to be greater than this value. Give one explanation for this discrepancy. Angular Momentum