A uniform, solid disk with mass m and radius R is pivoted about a horizontal axis through its center. A small object of the same mass m is glued to the rim of the disk. If the disk is released from rest with the small object at the end of a horizontal radius, find the angular speed when the small object is directly below the axis.

A ball (in the form of a spherical shell which has a moment of inertia of 2/3 M R^2) rolls down a roof, then falls to the ground. The ball has a mass of 1.65 g and a radius of 15.0 cm. The roof is inclined at 20.0 degrees and the ball rolls a distance of 3 meters along the roof before falling off. a)  What is the angular speed of the ball at the moment it leaves the roof? b)  If the distance from the end of the roof to the ground is 2.50 m, how many revolutions does the ball make before it hits the ground?

A thin rod has a length of 0.900 m and rotates in a circle on a frictionless tabletop. The axis is perpendicular to the length of the rod at one of its ends. The rod has an angular velocity of 0.607 rad/s and a moment of inertia of 1.06 x 10-3 kg-m². A bug standing on the axis decides to crawl out to the other end of the rod. When the bug (whose mass is 5 x 10-3 kg) gets where it's going, what is the change in the angular velocity of the rod? Number i Units

A figure skater is spinning with an angular velocity of +16.4 rad/s. She then comes to a stop over a brief period of time. During this time, her angular displacement is +3.65 rad. Determine (a) her average angular acceleration and (b) the time during which she comes to rest.

A cylinder has a cone removed from it.  The cylinder and the conical hole have the same radius (2.06 meters) and height (4.56 meters).  The cylinder has a density of 447 kg/m3. What is the rotational inertia of the cylinder with the cone removed in kg m2?  You can set your origin at the tip of the cone, which is also the center of the base of the cylinder.

A child jumps to the edge of a carousel, that is in the shape of a circular plate with a radius of 1.3 m and was rotating at an angular velocity of 1.2 s-1 before the chuld jumped on it. The weight of the carousels is 80 kg, the weight of the child is 22 kg. What is their angular velocity after the jump? Later, the child moves closer to the center of the carousel plate by 80 cm. What is the new angular velocity?

A thin rod has a length of 0.792 m and rotates in a circle on a frictionless tabletop. The axis is perpendicular to the length of the rod at one of its ends. The rod has an angular velocity of 0.939 rad/s and a moment of inertia of 1.41 x 103 kg-m². A bug standing on the axis decides to crawl out to the other end of the rod. When the bug (whose mass is 5 x 10-³ kg) gets where it's going, what is the change in the angular velocity of the rod?

A playground merry-go-round of radius R = 1.80 m has a moment of inertia I = 255 kg. m² and is rotating at 12.0 rev/min about a frictionless vertical axle. Facing the axle, a 23.0-kg child hops onto the merry-go-round and manages to sit down on the edge. What is the new angular speed of the merry-go-round? rev/min

A small 0.400-kg object moves on a frictionless horizontal table in a circular path of radius 3.30 m. The angular speed is 6.63 rad/s. The object is attached to a string of negligible mass that passes through a small hole in the table at the center of the circle. Someone under the table begins to pull the string downward to make the circle smaller. If the string will tolerate a tension of no more than 113N, what is the radius of the smallest possible circle on which the object can move?

A solid disk rotates in the horizontal plane at an angular velocity of 4.20 × 10-2 rad/s with respect to an axisperpendicular to the disk at its center. The moment of inertia of the disk is 0.14 kg.m2. From above, sand is droppedstraight down onto this rotating disk, so that a thin uniform ring of sand is formed at a distance of 0.40 m from the axis.The sand in the ring has a mass of 0.50 kg. After all the sand is in place, what is the angular velocity of the disk?