SP1. A merry-go-round in the park has a radius of 1.8 m and a rotational inertia of 900 kg-m². A child pushes the merry- go-round with a constant force of 80 N applied at the edge and parallel to the edge. A frictional torque of 12 N-m acts at the axle of the merry-go-round. a. What is the net torque acting on the merry-go-round about its axle? b. What is the rotational acceleration of the merry-go- round? c. At this rate, what will the rotational velocity of the merry-go-round be after 15 s if it starts from rest? What in d

2. A yo-yo consists of two solid disks, each of mass M and radius 3R. The two disks are connected by a rod of radius R and negligible mass. Assume the yo-yo starts at rest. a. Use the view on the right to draw the extended free body 3R diagram for the yo-yo. b. What is the moment of inertia of the yo-yo about an axis through its symmetry axis? м м c. Write Newton's 2nd law for the yo-yo. Choose your coordinate system carefully. d. Write the rotational form of Newton's 2nd law for the yo-yo. Treat the center of mass as being at the axis of rotation. Choose the positive direction of the rotation so a is positive. e. The point where the yoyo is momentarily at rest is where the string contacts the rod of the yo-yo. Use this to obtain a relation between the acceleration of the center of mass and the angular acceleration. f. Determine the linear acceleration of the yo-yo.

8. SITUATIONAL QUESTION At t = 0, a grinding wheel has an angular velocity of 25 rad/s. It has a constant angular acceleration of 32 rad/s2 until a circuit breaker trips at t = 2.5 seconds. From then on, it turns through 423 rad as it coasts to a stop at constant angular acceleration. Through what total angle did the wheel turn between t=0 and the time it stopped? a. 108rad b. 540rad c. 114rad d. 537rad At what time did it stop? a. 12.186 s b. 10.186 s c. 11.506 s d. 9.506 s A carousel is initially at rest. At t = 0, it is given a constant angular acceleration a 0.058 rad/s2, which increases its angular velocity for 9.0 s. At t = 9 s, determine the total acceleration of a child 3.5m from the center of the carousel. a. 0.975 m/s2 b. 0.954 m/s2 c. 0.957 m/s2 d. 0.945 m/s2 8i. 8ii. 8iii.

9. The picture below shows a rod of mass 4.50 kg which is free to rotate horizontally about one end at point O (the picture is a top view) with two forces acting on it as shown. a. What is the net torque on the rod due to the two F2 = 24.0 N F, = 12.0 N forces? b. What is the angular acceleration of the rod? If this angular acceleration remains constant and the rod is initially at rest, then what is the roď's kinetic energy 30.0% C. 2.50 m 3.50 m after 12.5 s? 10. The picture below shows a 1.75 kg box pressed against a spring whose spring constant is 275 N/m compressing the spring a distance of 0.225 m. When released the box slides along a frictionless surface and down a ramp. After reaching the bottom of the ramp, the box slides for a short distance before encountering a rough patch of floor where friction brings the box to a stop after 1.35 m. a. How fast is the box moving when it reaches the bottom of the ramp before encountering the rough patch? b. What is the magnitude of the…