Problem 7 Yo-yo Consider a yo-yo of mass m and radius R, and treat it as a solid disk. The string is coiled around the yo-yo at a radius R/2. We release the yo-yo while holding one end of the string. (a) How does the acceleration of the center of mass/gravity of the yo-yo relate to the angular acceleration of the yo-yo? (Make sure you decide which direction is positive for both the rotational motion and linear motion). (b) Start with free-body diagrams (extended and simple) to find the linear acceleration of the yo-yo.

A clock hangs on a wall. a) What is the direction of the average angular velocity of the seconds hand? b) What is the magnitude of the average angular velocity of the seconds hand?

Modern wind turbines generate electricity from wind power. The large, massive blades have a large moment of inertia and carry a great amount of angular momentum when rotating. A wind turbine has a total of 3 blades. Each blade has a mass of m = 5500 kg distributed uniformly along its length and extends a distance r = 44 m from the center of rotation. The turbine rotates with a frequency of f = 12 rpm. a)Calculate the total moment of inertia of the wind turbine about its axis, in units of kilogram meters squared.  b)Enter an expression for the angular momentum of the wind turbine, in terms of the defined quantities.  c)Calculate the angular momentum of the wind turbine, in units of kilogram meters squared per second.

A diver performs a flip in the air. The radius of gyration is 0.43 when the diver initially leave the board and the diver is rotating at an angular velocity of 6.3 rad/sec. What is the linear velocity of the head when they decrease their radius of gyration to 0.24. The distance from the head to the center of gravity of the individual is 0.3 meters?

A 7.83 kg particle with velocity = (1.81 m/s )i - (9.64 m/s ) is at x = 8.83 m.y = 1.23 m. It is pulled by a 9.44 N force in the negative x direction. About the origin, what are (a) the particle's angular momentum, (b) the torque acting on the particle, and (c) the rate at which the angular momentum is changing? (a) Number (b) Number (c) Number : Units Units Units

A 20-kg child running at 1.4 m/s jumps onto a playground merry-go-round that has mass 180 kg and radius 1.6m. She is moving tangent to the platform when she jumps and she lands right on the edge. What is the angular velocity of the child and the merry-go-round if the merry-go-round started from rest? You can treat the merry-go-round as a solid disc and ignore any friction in its axle. Please answer in units of rad/sec.

A 10 kg cylindrical barrel with a radius of 0.5 m rotates about a vertical axis of rotation without displacing with an initial angular velocity of 4 rad/s. The rotational inertia of the cylindrical barrel is 0.3mr2 and rain begins to fill the barrel with water as its rotating. If the barrel accumulates 4 kg of water, calculate the new angular velocity of the barrel.

A kid runs towards the edge of a merry-go-round that is not rotating and jumps on. The merry-go-round then rotates with a constant angular velocity ω. Assume that the kid has a mass of 40 kg and is initially running at a speed of 4 m/s tangent to the edge of the merry-go-round. The merry-go-round is a uniform disk with a mass of 80 kg and a radius of 2 m. Assume that it rotates without friction. What is the final angular velocity ωf (in radians/s) of the merry-go-round (with the kid riding)?

A volley ball players 4.4 kg arm moves at an average angular velocity of 16 rad/s during the execution of a spike. if the average moment of inertia of the extending arm is 0.39 kg*m^2. what is the average radius of rotation for the arm during the spike?

A light rigid bar of length, l = 1m, is attached to two particles, with masses m1 = 4 kg and m2 = 3 kg, at their ends. The combination rotates in the xy plane about an axis through the center of the bar, right figure. Determine the angular momentum of the system about the origin when the speed of each particle is 5 m / s.