An aluminum cylinder of radius 12m, length of 20m, and thickness of 0.02m is spinning in space at the rate of once every 137 seconds around the y-axis. What is it's angular momentum and rotational kinetic energy?

A 20-kg child running at 1.4 m/s jumps onto a playground merry-go-round that has mass 180 kg and radius 1.6m. She is moving tangent to the platform when she jumps and she lands right on the edge. What is the angular velocity of the child and the merry-go-round if the merry-go-round started from rest? You can treat the merry- go-round as a solid disc and ignore any friction in its axle. Please answer in units of rad/sec.

After all the metal has unwound from the roller, the student measures the radius R and the angular speed wo of the roller to be 25 cm and 20 rad/s respectively. Observed from the side, the roller rotates counterclockwise, as shown. A piece of clay of mass m strikes the very bottom edge of the roller with a horizontal velocity v = 4.0 m/s. The clay sticks to and rotates with the roller. The clay-roller system then rotates with a final angular velocity wi. (f) Is wi greater than, less than, or equal to wo? Justify your answer.

A barbell consists of two small balls, each with mass 400 grams (0.4 kg), at the ends of a very low mass rod of length d = 45 cm (0.45 m). The center of the barbell is mounted on the end of a low mass rigid rod of length b = 0.675 m (see Figure), and this rod rotates clockwise with angular speed 140 rad/s. In addition, the barbell rotates clockwise about its own center, with an angular speed 120 rad/s.

A bullet with mass of 25 grams traveling at speed of 185m/s hits the end of a rod as shown.  The rod has a mass of 3 kg and a length of 80 cm, and it is free to spin about a perpendicular axis located at its center.  If the bullet remains stuck in the end of the rod, what will be the angular speed of the rod after the bullet hits it?  Let MM be the mass of the rod and mm be the mass of the bullet. The moment of inertia of a rod rotating about a perpendicular axis through its center is (1/12)ML2.(1/12)ML2.  (Hint: After the bullet is embedded in the rod, it contributes m(L/2)2m(L/2)2to the moment of inertia of the rod.)

A solid uniform spherical boulder travels down a hill. At the top of the hill the boulder is rolling with a horizontal speed of 5 m/s. The top half of the hill is rough, so that the boulder continues to roll without slipping. The bottom half of the hill and the valley is covered in smooth ice, so that there is no static friction between the boulder and the hill. How fast is the boulder moving when it gets to the bottom of the hill? What is its rotational speed in the valley if the boulder has a radius of 10 cm? Rough 50.0 m Smooth

The diameters of the main rotor and tail rotor of a single-engine helicopter are 7.59 m and 0.98 m, respectively. The respective rotational speeds are 456 rev/min and 4143 rev/min. a) Calculate the speeds of the tips of both rotors. b) Compare these speeds with the speed of sound, 343 m/s.

A figure skater is spinning with an angular velocity of +10.3 rad/s. She then comes to a stop over a brief period of time. During this time, her angular displacement is +4.97 rad. Determine the time during which she comes to rest.

A light rod of length ℓ = 1.00 m rotates about an axis perpendicular to its length and passing through its center as in the figure below. Two particles of masses m1 = 4.50 kg and m2 = 3.00 kg are connected to the ends of the rod. Just need answer to (b), got 2.84 and said that was wrong.  (a) Neglecting the mass of the rod, what is the system's kinetic energy when its angular speed is 2.60 rad/s? 6.34 J  (b) Repeat the problem, assuming the mass of the rod is taken to be 1.90 kg.

A uniform ring with the mass of 4 kg and a radius of 20 cm is rotating at a rate of 20 rad/s. What is the angular momentum of the ring?