A block of mass m = 0.65 kg, moving at constant speed v = 5.00 m/s, slides along a horizontal, frictionless surface and collides with and sticks to the end of an initially vertical, stationary thin rod, of mass M = 5.00 kg, and length L = 0.50O m. See the figure below. The other end of the rod is attached to a horizontal frictionless pivot which allows the mass-rod system to rotate to an angle 0 with the vertical direction. What is the maximum angle 0max the rod makes with the vertical? (The moment of inertia of a uniform thin rod about an axis through one end is given by ML2/3) L

A block of mass m = 0.75 kg, moving at constant speed v = 4.00 m/s, slides along a horizontal, frictionless surface and collides with and sticks to the end of an initially vertical, stationary thin rod, of mass M = 5.50 kg, and length L = 0.750 m. See the figure below. The other end of the rod is attached to a horizontal frictionless pivot which allows the mass-rod system to rotate to an angle θ with the vertical direction. What is the maximum angle θmax the rod makes with the vertical? (The moment of inertia of a uniform thin rod about an axis through one end is given by ML2/3)

The figure shows a small particle of mass 0.278 kg that is moving with a speed of 7.29 m/s when it collides and sticks the the edge of a uniform solid cylinder. The cylinder is free to rotate about an axis through its center. The cylinder has a mass of 2.677 kg, and a radius of 0.28 m, and is initially at rest. What is the angular velocity of the system after the collision? Express your answer in radians/s to 3 significant figures. Before After

A uniform solid disk of mass m = 2.99 kg and radius r = 0.200 m rotates about a fixed axis perpendicular to its face with angular frequency 6.05 rad/s. (a) Calculate the magnitude of the angular momentum of the disk when the axis of rotation passes through its center of mass. kg • m2/s (b) What is the magnitude of the angular momentum when the axis of rotation passes through a point midway between the center and the rim? kg • m2/s

A thin rod of length 2.95 m and mass 13.3 kg is rotated at an angular speed of 3.95 rad/s around an axis perpendicular to the rod and through its center of mass. Find the magnitude of the rod's angular momentum. kg •m?/s

A playground merry-go-round has a radius of R = 4.0 m and has a moment of inertia Icm = 7.0 x 10³ kgm² about an axis passing through the center of mass. There is negligible friction about its vertical axis. Two children each of mass m = 25 kg are standing on opposite sides a distance ro = 3.0 m from the central axis. The merry-go-round is initially at rest. A person on the ground applies a constant tangential force of F= 2.5 x10² N at the rim of the merry-go-round for a time At =1.0 x 10¹ s. اناما R a. What is the magnitude of angular acceleration of the merry-go-round? b. What is the angular speed of the merry-go-round when the person stopped applying the force? c. What is the rotational kinetic energy of the merry-go-round when the person stopped applying the force? d. The two children then walk inward and stop a distance of r1 =1.0 m from the central axis of the merry-go-round. What is the angular velocity of the merry-go- round when the children reach their final position? What is…