A skater spins with an angular speed of 12.0rad/s with his arms outstretched. He lowers his arms, decreasing his moment of inertia from 41kgm' to 36kgm2. a. Calculate his initial and final rotational kinetic energy. b. Does his rotational kinetic energy increase or decrease? c. What causes this change in kinetic energy?
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- In order for an object to roll smoothly (with constant angular acceleration) down a ramp, it must have either spherical or cylindrical symmetry. Consider spherically and cylindrically symmetric objects with mass M and outer radius R rolling without slipping down an incline of height h and angle 0 from the horizontal. The rotational inertias of such objects can be written in the generalized form: / = cM R² , where c is a shape factor whose value depends on the geometry of the object. (If you look at the table of rotational inertias in the textbook you'll be able to see that this is true.) (For this question, consider M, R, c, h, 0, and g as the given quantities-express your answers in terms of some or all of these quantities. Simplify your answers as much as you can.) M. If the object starts from rest at the very top of the ramp before rolling freely down a. the ramp without slipping, find the object's (linear) speed at the bottom of the ramp. (Hint: use conservation of energy.) VpottomThe Tasmanian Devil has a twist angular momentum which increases from 0 to 50kg·m2/s in 0.25 s as he initiates a twisting jump (his famous tornado). During this 0.25 s,his moment of inertia about his twisting axis is 2.2 kg·m2.a. How large is the average torque that produces this change in angular momentum?b. How fast is his twist angular velocity at the end of the 0.25 s?A 200 NmA drum major twirls a 95-cm-long, 440 g baton about its center of mass at 140 rpm. What is the baton's rotational kinetic energy? Express your answer to two significant figures and include the appropriate units.
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- You and your friend ride a merry-go round. You sit further away from center (2r) but your friend sits closer to the center (r). If the angular speed of the system is a constant, what can you say about following for you and your friend?a. linear speed? b. Angular speed?c. radial acceleration?b. tangential acceleration? 2c. if the ride starts with zero angular speed and run with constant angular acceleration of 2.00 rad/sradius 4m circle., calculate final angular displacement and linear displacement you and your friend travel?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.A typical small rescue helicopter has four blades: Each is 4.00 m long and has a mass of 50.0 kg. The blades can be approximated as thin rods that rotate about one end of an axis perpendicular to their length (I = (Ml^2)/3). The helicopter has a total loaded mass of 1000 kg. a.) Calculate the rotational kinetic energy in the blades when they rotate at 300 rpm. b.) Calculate the angular momentum of the four combined blades when they rotate at 300 rpm (Hint: Find the angular momentum for one blade and multiply it by 4).
- The angular velocity of a rigid body is shown in the graph below. What is its angular displacement between t = 0 and t = 4 s? a.20 rad b.80 rad c.60 rad d.40 radA cylindrical shell (I = MR2), a solid cylinder (I =1/2 MR2), and a solid sphere (I =2/5 MR2) all having the same radius is made to roll on a frictionless ramp with an angle θ from the horizontal. Which of these objects will be the last to reach the bottom of the ramp, if they started to roll without slipping from the same height? a. cylindrical shellb. solid cylinderc. solid sphered. Not enough information is givenA metal disc in a playground with a mass of 45 kg and a diameter of 4 meters is rotating on its central frictionless axis with an initial angular velocity of 3 rad/s. A child with a mass of 14 kg suddenly jumps unto the disc and stands on the edge. a.What is the new angular velocity of the disc with the kid on it? b. What is the tangential velocity of the kid as he rides the disc?