Miscellaneous Rotation

More interesting relationships

Momentum Formula for Kinetic Energy Often it is useful to have the formulas for kinetic energy written in terms of momentum.

Conservation of Angular Momentum Practice Problem 1 A disk is rotating with speed    about a frictionless shaft. Its rotational inertia is I 1. It drops onto another disk of rotational inertia I 2 that is at rest on the same shaft. Because of friction, the two disks attain a common speed  f. Find  f.

Conservation of Angular Momentum Practice Problem 2 A merry-go-round (r =2, I = 500 kg m/s 2 ) is rotating about a frictionless pivot, making one revolution every 5 s. A child of mass 25 kg originally standing at the center walks out to the rim. Find the new angular speed of the merry-go- round.

Conservation of Angular Momentum Practice Problem 2 A merry-go-round (r =2, I = 500 kg m/s 2 ) is rotating about a frictionless pivot, making one revolution every 5 s. A child of mass 25 kg originally standing at the center walks out to the rim. Find the new angular speed of the merry-go- round. Ans.-  f =(5/6)  i

Conservation of Angular Momentum Practice Problem 3 The same child as in the previous problem runs with a speed of 2.5 m/s tangential to the rim of the merry go round, which is initially at rest. Find the final angular velocity of the child and merry go round together.

Conservation of Angular Momentum Practice Problem 3 The same child as in the previous problem runs with a speed of 2.5 m/s tangential to the rim of the merry go round, which is initially at rest. Find the final angular velocity of the child and merry go round together. Ans.  = rad/s

Conservation of Angular Momentum Practice Problem 4a A particle of mass m moves with speed v 0 in a circle of radius r 0. The particle is attached to a string that passes through a hole in the table. The string is pulled downward so the mass moves in a circle of radius r. Find the final velocity.

Conservation of Angular Momentum Practice Problem 4a A particle of mass m moves with speed v 0 in a circle of radius r 0. The particle is attached to a string that passes through a hole in the table. The string is pulled downward so the mass moves in a circle of radius r. Find the final velocity. Ans. v= (r 0 /r) v 0

Conservation of Angular Momentum Practice Problem 4b Find the tension T in the string in terms of m, r, r 0 and v o.

Conservation of Angular Momentum Practice Problem 4b Find the tension T in the string in terms of m, r, r 0 and v o.