7. Two discs are initially spinning in opposite directions. The upper disc has rotational inertia of 10kgm? and a rotation rate of 12rad/s. The lower disc has rotational inertia of 25kgm² and a rotation rate of 8rad/s. The upper disc is dropped onto the lower disc and they stick together. What is the rotation rate AND direction of the two disc system?

4. A cylinder with mass m1 = 2.5 kg and radius r = 20 cm rotates counterclockwise about a vertical axis through its center with angular speed @1=5.0 rad/s. A second cylinder with mass m₂ = 1.0 kg and radius r1= 15 cm rotates clockwise about the same axis with angular speed @2 = 12 rad/s. The upper cylinder is lowered onto the lower one and they couple so they have the same rotational axis. Find the angular speed of the combination. Is kinetic energy conserved? If not, what happened to the a) b) kinetic energy? m₂ = 1.0 kg T2 = 15 cm m₁ = 2.5 kg n W₂ = 12 rad/s T₁ = 20 cm w₁ = 5 rad/s

A mass on the end of a 0.50 m long string is spun overhead with a velocity of 3.5 m/s. What is the angular velocity of the mass? 0.14 rad/sec 1.17 rad/sec 7.00 rad/sec 24.5 rad/sec t 9964

2. Two students perform a simple experiment. The first student observes the orientation of a stationary disk with a single mark on the edge of the rim. He then looks away. The secondstudent then gives the disk a constant rotational acceleration of 3.0 rad/s2 for a time of 4.0 seconds; she then brings the disk to a halt with constant angular acceleration in a time of 0.10 s. The first student is now allowed to look at the disk again. (a) From the point of view of the first student, through what angle did the disk move? (b) What was the average angular velocity of the disk?

5. The disk has an angular acceleration a = 8 rad/s' and angular velocity w = 3 rad/s at the instant shown. If it does not slip at A, determine the magnitude and direction of the acceleration of point B. w = 3 rad/s a = 8 rad/s? 45° 0.5 m 45° B

1. A wheel rotating about a fixed axis at a constant angular acceleration has an angular velocity of 2.00 rad/s. Two seconds later it has turned through complete revolutions. What is the angular acceleration of this wheel? 5.00 2. A jet engine, starting from rest, is accelerated at a rate of 5.00 rad/s². After 15.0 seconds, what is the angular velocity of the engine? What is the total angular displacement over this period of time? 3. A merry-go-round is traveling initially with an angular velocity of 5.00 rad/s. A child pushes the merry-go-round over 10.0 revolutions, causing the merry-go-round to accelerate at a constant rate of 1.00 rad/s². What is the final angular velocity of the merry-go-round? 4. An object moves in a circle of radius 2.00 m with instantaneous angular velocity of 5.00 rad/s and angular acceleration of 4.00 rad/s². What is the magnitude of the linear acceleration felt by the object? 5. A fan takes 2.00 s to reach its operating angular speed of 10.0 rev/s. What is…

3. A disk accelerates from rest to an angular velocity of 600 rad/s in 3.0 s. (a) What constant angular acceleration does it have? (b) How many revolutions did you make in that time?

19. A wheel 1.00 m in radius is rotating at 100 rad/s. The wheel accelerates uniformly from 100 rad/s to 500 rad/s in 100 revolutions. Determine the  Rate of angular acceleration Time required for the wheel to accelerate to 500 radians per second Tangential acceleration of a point on the rim as the wheel is accelerating Radial acceleration of a point on the rim before acceleration begins

3. A rod with a mass of 10kg and a total length of 2 meters that can spin about an axis through its center ( I = ML2 ) receives a constant force of 5 N on one of its ends. As the rod spins, the 12 force will maintain the same strength and orientation i.e., angled at 60 degrees with respect to the rod. The rod is initially at rest. Total Length Axis 60 deg F, a. How many radians does the rod sweep through after a period of 10 seconds? b. What is the speed of a point on the end of the rod at that same moment?

1. A point on the outer rim of a hollow disk (I = mr2) with radius r and mass m rotates with a constant angular speed of ω. How far will the point travel (in meters) in 1 minute of rotation? Let w=11.5 rad/s and r=0.78m a. how many revolutions will the point experience during this time? b. What net torque is necessary to stop the disk in time t? Let t=7 sec and m =14kg