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AP Physics 1 U11 - WS 1 - Rotation page 1 Unit 11 - Rotational Dynamics 5/3/21 1. In the image to the right, a satellite is made to spin using four tangential rockets. The satellite has a mass m and a radius R and can be modeled as a solid cylinder with moment of inertia l = =mR" a. What is the required force of each rocket if the satellite is to reach 33 rpm in 5.0 minutes? b. What was the change in the angular momentum of the satellite during this time? C. If the satellite's radius were twice as big, by what factor would each rocket have to be changed to achieve the same effect as in part (a)? How would this affect the final angular momentum of the satellite? d. If the satellite were twice as massive, by what factor would each rocket have to be changed to achieve the same effect as in part (a)? How would this affect the final angular momentum of the satellite? 2. You stand with your hands at your side on a platform that is rotating at a rate @. If you raise your arms to a horizontal position, the rotational speed decreases to % @. a. Why does this happen? b. By what factor has your moment of inertia changed? C. What would have happened if you had raised only one arm? d. How would raising your left leg (in addition to your arms) parallel to your left arm affect your rotational speed? 3. A uniform rod of mass M and length L can pivot freely (ignore friction) about a hinge attached to a wall. The rod is held horizontally and then released. Assume that the force of gravity acts at the center of mass of the rod. (The moment of inertia for THIS CM rod is - ML-) a. What is the angular acceleration of the rod the moment it's released? Me b. What is the linear acceleration of the tip of the rod at this moment? 4. A cyclist accelerates from rest at a rate of 1.00 m/s How fast will a 1= ? point on the rim of the tire (that has a diameter of 68 cm) at the top be moving after 3.0 s? (Hint: At any moment, the lowest point on the tire is a = 1.00 m/2 in contact with the ground and is at rest.) This point on tire Problems 5-7: A ball and a block with equal masses are released from the at rest momentarily same height and slide down ramps with identical shapes. The ball rolls without slipping and the block slides without friction. 5. Which object has a greater total mechanical energy when it leaves its ramp? Explain. 6. Which object has a greater linear speed at the bottom of its ramp? Explain. 7. Which object travels higher after leaving its ramp? Explain. 8. A 50 kg boy and a 40 kg girl sit at opposite ends of a 3m long, 20 kg seesaw. How far from the girl should the fulcrum be placed so that the two kids balance