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FA#7—Angular Momentum AP Physics/MTHS/Matthews Name ___________________________ Directions: Answer the following questions on this sheet of paper. Show all work. (1) Fill in the following table for the missing quantities with units. The table represents the rotational inertia and angular speed and momentum of a student spinning on a wheel. Rotational Inertia (I) 0.4 0.8 0.4 Rotational Velocity (ω) 2π π/2 Rotational Momentum (L) 2.5 2.5 2.5 (2) A student (I = 0.4 kgm2) is spinning on a spinning chair with a rotational speed of 2π rad/sec when another student exerts a torque on her with a force of 10 N for 2 seconds at a distance of 0.5 m from her axis of rotation in the CCW direction. What will be her new angular momentum just after the push? (3) The same student pushes the first student with the same force at the same radius for the same time but in the CW direction. What will be her new angular momentum just after the push? Which direction will she be spinning after the push? (4) A 0.2 kg block (I = mR2) is spinning on a frictionless table while attached to a 0.5 m string that causes it to rotate in a circular path. The block’s initial rotational speed is 2.0 rad/s. What will be the block’s new rotational speed if it is pushed with a force of 2 N tangent to the path for 2 seconds? (5) For # 4 assume that while the string pulls on the puck it is pulled downwards through a hole in the table at the axis of rotation. How will this change affect the rotational inertia of the system? How will this change affect the rotational momentum of the system? How will the change affect the rotational speed of the system? Explain. (6) Determine the rotational speed and tangential speed of the block when the string is 0.20 m from the axis. (no external force is applied to the block here). (7) Complete the following sentence, when an external torque acts on a system the angular momentum _____________ but when no external torque acts on a system in motion then the angular momentum_____________________. (8) An ice skater (I = 0.40 kgm2) spins at a rate of 2π rad/s when she extends her arms such that her rotational inertia doubles. What will be her new rotational speed? (9) If the ice skater were holding weights in her hands her new I = 0.80 kgm2 with her arms in. If she rotates at 2π rad/s with the weights in, when she extends her arms and doubles her “I”, what will be her new rotational velocity? Show math to prove your point. (10) Imagine that our sun ran out of nuclear fuel and collapsed. What would its radius have to be in order for its period of rotation to be the same as “pulsars” with a rotational period of 1.33 seconds/rotation? The sun’s current period of rotation is 25 days. (I = 2/5mR2 for spheres). Msun = 2.0 x 1030 kg. Rsun = 0.70 x 109 m) (confirm r = 550,000 m). (11) If more weight is dropped into the skater’s arms her rotational speed will decrease noticeably; however, if she simply drops a weight her rotational speed seems not to change at all? Explain why. Use Angular Momentum bar charts to prove your point or Newton’s 3rd law. (12) A playground carousel rotates freely, with a moment of inertia of 125 kgm2 (without riders). When a girl is standing on the carousel 1.50 m from the center, the carousel has an angular velocity of 0.60 rad/s. However, as the child moves inward to a point located 0.75 m from the center, the angular velocity increases to 0.80 rad/s. Assuming the child can be treated as a point object, what is her mass?