Let there be a disk shaped merry-go-round of radius R = 2m and mass M = 90 kg with a 30 kg child riding on at the outer edge. It spins at a rate of 2 revolutions per second with the child on it. a. What is the initial angular velocity? b. If the child falls off, what is the new angular velocity? (hint use conservation of angular momentum)

A monkey has a 50 cm long tail swinging through circular arcs.  a. The moneky prepares to swing through a semicircular arc by grabbing a branch 50 cm in front.What is the angular acceleration as she begin to drop? b. What is the monkeys linear speed at the bottom of this arc, 50 sm below starting point? What is her angular speed? c. The monkey has a mass of 10 kg. What is the tension in her tail at the bottom of the arc?

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? d. What is the rotational acceleration of the merry-go- round if the child stops pushing after 15 s? How long will it take for the merry-go-round to stop turning?

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?

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.

5. A 108 cm, 0.73 kg golf club is swung from rest for 0.5 seconds with a constant acceleration of 10 rad/s2.a. What is the angular velocity of the club head when it impacts the ball? b. What is the angular momentum of the club head when it impacts the ball?  please show all steps, work, and formulas

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A disk is initially rotating counterclockwise around a fixed axis with angular speed w0. Answer the questions below.  A. What is the net torque acting on the disk if the radius is 0.6 m? B. If the moment of inertia of the disk is 4kg ∙ m^2, what is the angular acceleration of the disk? C. If the initial angular velocity is 6 rad/s counterclockwise, what is the angular velocity after 10 seconds? D. What happens to the angular velocity of the disk over time? Sketch a graph!

The rotating blade of a blender turns with a constant angular acceleration 1.50(rad/s²]. A. How much time does it take to reach an angular velocity of 36. 0 [rad/s] starting from rest? Through how manry revolutions does the blade turn in this time interval? C. What are the tangertial acceleration and tangential speed of an ant sitting on the blade 10.0 [cm) from the axis of rotation during the end of this irterval? D. What is the moment of inertia ofthe ant if its mass is 10.0 (g? E. What is the rotational kinetic energy of the ant? B.

A ship's wheel can be approximated as an annular cylinder (different from a ring) of mass 6.7 kilograms, inner radius 25 centimeters, and outer radius 32 centimeters; and eight spokes of mass 0.50 kilograms and length 49 centimeters.   a. What is the moment of inertia? Include units in your answer. More information. b. Disagreeing over which way to go, the captain and the helmsman try to turn the wheel in opposite directions. The captain applies a force of 311 newtons at the inner radius, while the helmsman applies a force of 287 newtons at the outer radius. What is the magnitude of the angular acceleration of the wheel? Include units in your answer.