A solid cube of wood of side 2a and mass M is resting on a horizontal surface. The cube is constrained to rotate about a fixed axis AB (Fig. P11.64). A bullet of mass mand speed v is shot at the face opposite ABCD at a height of 4a/3. The bullet becomes embedded in the cube. Find the minimum value of v required to tip the cube so that it falls on face ABCD. Assume m<< M. C 2a D 4a 3 B A Figure P11.64

A uniform thin rod of length 0.70 m and mass 5.5 kg can rotate in a horizontal plane about a vertical axis through its center. The rod is a rest when a 3.0-g bullet traveling in the horizontal plane of the rod is fired into one end of the rod. As viewed from above, the direction of the bullet velocity makes an angle of 60° with the rod (see the figure). If the bullet lodges in the rod and the angular velocity of the rod is 11.0 rad/s immediately after the collision, what is the magnitude of the bullet's velocity just before impact?

A 550.0 g bird is flying horizontally at 2.50 m/s, not paying much attention, when it suddenly flies into a stationary vertical bar, hitting it 25.0 cm below the top. The bar is uniform, 0.700 m long, has a mass of 1.50 kg kg, and is hinged at its base. The collision stuns the bird so that it just drops to the ground afterward (but soon recovers to fly happily away). What is the angular velocity of the bar just after it is hit by the bird? Express your answer in radians per second. W1 = rad/s

Two identical tops, #1 and #2, spin with angular velocities ω1 = 10 rad/s counterclockwise and ω2 = 12 rad/s clockwise. The tops bump into one another and separate. After the collision, the first top has angular velocity of 5 rad/s counterclockwise. During the collision, the force of impact is along the line connecting the centers of the top, so no torque is exerted on either top. What is the magnitude of the angular velocity of the second top? Does the top spin clockwise or counterclockwise?

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…