(1) Please show the relations (use as many paper sheets as you need). 1. [4] 2. [4](2) Compute the quantities below. (Express answers to 3 sig. figs.) [16] 1. Hanging mass's acceleration a = m/s2 2. String tension T = N 3. Torque exerted on disk t = N.m 4. Disk's moment of inertia l = kg.m2 5. Hanging mass's initial potential energy U =_ 6. Hanging mass's final velocity Uh = m/s 7. Hanging mass's final kinetic energy Kh = 8. Disk's final rotational kinetic energy Ka = (3) Compute the quantities below. (Express answers to 3 sig. figs.) [6] 1. Initial angular momentum Li = kg.m /s 2. Initial rotational kinetic energy Ki = 3. Final angular velocity Of =_ rad/s 4. Final rotational kinetic energy Kf =_Translational Rotational v = Vo + at W = wot at Ax = Vot + (1/2)at2 AO = Wot + (1/2)at2 (1) v2 = VO2 + 2ax Ax W 2 = Wo2 + 20 x 40\ft = la, (2)Hanging mass Rotating object F = Wh -T = mna, T= rT = Ia (3)\f(5) Krot = NIU + Ktran + Krot = constant, (6)\f(1) Considering the setup in Figure 2, please use Eqs. (3}(5) to show that 1. The torque exerted on the rotating object is I" = mhr(g m\"). (9) 2. The total kinetic energy of the system is Km = $0 + mhrowz (10) In this lab, we will use these relations to compute key quantities from the measurements. For example, we will use the measured mm 1", and a to compute the torque 1', and then the moment of inertia as I = r/a. (2) In a real experiment with the setup of Figure 2, initially the disk is at rest, and the hanging mass is placed 0.500 m above the floor. Then the hanging mass falls down until finally touches the floor. Measurements show the hanging mass mh = 0.115 kg, the spindle radius r = 0.0251m, the disk's angular accleration o: = 3.551 rad/$2, and the disk's final angular velocity (of = 11.29 rad/s. Please compute the quantities below to 3 sig. figs.: (hint: properly use Eqs. (1) (10) .Take 9 = 9.80 m/sz.) 1. Hanging mass's acceleration a 6. Hanging mass's final velocity 1711 (from 2. String tension '1" the measured (of) 3. Torque exerted on disk I 7. Hanging mass's final kinetic energy Kh 4. Disk's moment of inertia I 8. Disk's final rotational kinetic energy Kd 5. Hanging mass's initial potential energy U (3) A disk with moment of inertia 7.15 X 10'3 kg-m2 initially rotates about its center at angular velocity 5.32 rad/s. A non-rotating ring with moment of inertia 4.26 X 103 kg-m2 right above the disk's center is suddenly dropped onto the disk. Finally, the two objects rotate at the same angular velocity (of about the same axis. There is no external torque acting on the system during the collision. Please compute the system's quantities below to 3 sig. figs. 1. Initial angular momentum L1- 3. Final angular velocity (of (computed from L1) 2. Initial rotational kinetic energy K1- 4. Final rotational kinetic energy Kfrom 00f)