A solid and uniform disk of mass 8.0 kg and radius 25 cm is rotating at 1506 revolutions per minute (rpm) about an axis that goes through its center and perpendicular to the disk plane. A small particle of mass m is dropped vertically onto the disk, at a location 11.9 cm from the centre and moves together with the disk. The rotational speed of the setup is reduced to 1139 rpm. Find m (in unit of kg). The moment of inertia of a uniform disk around its rotational

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The figure shows three uniform solid disks, each of mass 9.4 kg and radius 0.5 m rotating independently around a common axle. Two of the disks rotate in one direction at 5.3 rad/s while the other rotates in the opposite direction at 3.5 rad/s. Calculate the magnitude of the system's angular momentum about a point in the middle of the center disk. L = kg m²/s .

A solid cylinder of mass 4 kg and radius 2 m rotates with constant angular velocity of 5 rad/s about an axis through its center. What is the angular momentum of the cylinder?

A lump of putty (0.050 kg) hits a contraption that is made of a uniform solid cylinder rotating about its center of mass and two rods that are attached to the sides of the cylinder.  The moment of inertia of the contraption is 0.250 kg∙m2.   After the collision, the putty attaches to the contraption 0.15 m from the axis of rotation and the combination is rotating at 1.0 rad/s. Determine the linear speed of the putty before the collision. Determine the angular impulse on the putty and on the block separately to show that they follow Newton’s 3rd law. How much energy is lost in the collision?  Where did it go?

In the figure, a 7.90 g bullet is fired into a 0.430 kg block attached to the end of a 0.140 m nonuniform rod of mass 0.578 kg. The block-rod-bullet system then rotates in the plane of the figure, about a fixed axis at A. The rotational inertia of the rod alone about A is 0.0761 kg·m2. Treat the block as a particle. (a) What then is the rotational inertia of the block-rod-bullet system about point A? (b) If the angular speed of the system about A just after impact is 3.64 rad/s, what is the bullet's speed just before impact?

A steel disc with a mass of 1.505 kg and a diameter of 8.00 cm is rotating with angular speed 4.75 rad/s. A second, aluminum disc of the same diameter but with mass 527 g and rotating with angular speed -0.07 rad/s is dropped on to the steel disc and both come to a common angular speed. What is this final angular speed?

A solid disk rotates in the horizontal plane at an angular velocity of 0.0652 rad/s with respect to an axis perpendicular to the disk at its center. The moment of inertia of the disk is 0.113 kg·m2. From above, sand is dropped straight down onto this rotating disk, so that a thin uniform ring of sand is formed at a distance of 0.393 m from the axis. The sand in the ring has a mass of 0.487 kg. After all the sand is in place, what is the angular velocity of the disk?

A solid, horizontal cylinder of mass 13.4 kg and radius 1.00 m rotates with an angular speed of 7.50 rad/s about a fixed vertical axis through its center. A 0.250-kg piece of putty is dropped vertically onto the cylinder at a point 0.900 m from the center of rotation and sticks to the cylinder. Determine the final angular speed of the system.  rad/s=

A student holds a spinning bicycle wheel while sitting motionless on a stool that is free to rotate about a vertical axis through its center (see the figure below). The wheel spins with an angular speed of 16.1 rad/s and its initial angular momentum is directed up. The wheel's moment of inertia is 0.130 kg · m2 and the moment of inertia for the student plus stool is 3.10 kg · m2. Apply conservation of angular momentum. A)Find the student's final angular speed (in rad/s) after he turns the wheel over so that it spins at the same speed but with its angular momentum directed down. ___________rad/s   B)Will the student's final angular momentum be directed up or down?