A 3.0-kg mass slides on a frictionless horizontal surface with a speed of 3.0 m / s when it collides with a 1.0-kg mass initially at rest as shown in the figure. The two masses stick to each other and slide on a frictionless circular wheel portion of radius 0.40 m. At what maximum height h, above the horizontal, do the masses reach? Answers: a) 0.18 m       b) 0.15 m      c) 0.21 m      d) 0.26 m        e) 0.40 m

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 pellet gun is fired at a solid disk that is free to rotate about a fixed horizontal axis, as shown in Figure 8-63. The disk is 21 cm in diameter and has a mass of 370 g. The pellet (m = 30.0 g) gets lodged in the disk and causes it to spin at a rate of 11 rad/s. Find the speed of the pellet just before it hits the wheel.

An isolated system consists of a single object, which initially moves without friction at velocity ux along a horizontal x-axis. After an internal explosion, the object splits into two parts, A and B. The figure shows the masses and speeds of these parts immediately after the explosion. None of these objects rotates. 1.50 m s-¹ 2.00 kg A Final kinetic energy initial kinetic energy 3.50 m s-¹ - 3.00 kg What is the difference between the total final kinetic energy of A and B and the initial kinetic energy of whole object? Give you answer by entering a number, specified to an appropriate number of significant figures, into the empty box. B J.

A new design for a race car is to have a large solid disk-shaped flywheel within the car storing kinetic energy. The uniform flywheel has mass 370 kg with a radius of 0.500 m and can rotate up to 230 rev/s. Assuming all of this stored kinetic energy could be transferred to the linear velocity of the 1200 kg car, find the maximum attainable speed of the race car. (in m/s)

Q4.) A 10 g bullet traveling at 450 m/s strikes a 10 kg, 820 mm-wide door at the edge opposite the hinge. The bullet embeds itself in the door, causing the door to swing open. How long does it take for the door to swing open 90° assuming negligible friction at the hinge? Q5.) A merry-go-round spins with a period of 1 second. It consists of a cylindrical disk with m=100 kg and radius = 1.5 m. You jump on the merry-go-round with a running start. Draw a picture to indicate where you should aim to land on the merry-go-round and the best angle of approach in order to achieve the largest possible change in angular momentum. If you weigh 70 kg, what is the minimum speed you must run in order to make it spin with the same speed in the opposite direction?

A track is mounted on a large wheel that is free to turn with negligible friction about a vertical axis (figure below). A toy train of mass m is placed on the track and, with the system initially at rest, the train's electrical power is turned on. The train reaches speed 0.20 m/s with respect to the track. What is the wheel's angular speed if its mass is 1.2m and its radius is 0.45 m? (Treat it as a hoop, and neglect the mass of the spokes and hub.) rad/s

Under some circumstances, a star can collapse into an extremely dense object made mostly of neutrons and called a neutron star. A star with a of mass of 2.0x1032 kg and radius 7.0x108 m is initially rotating at a rate of once every 30 days. The star collapses into a neutron star with the same mass but a new radius of 16,000 m. What is the angular speed of the star? (Give your answer in rotations per second.) Assume the star is a solid sphere: Isphere = 2/5 MR2.   The Crab Nebula (shown below) formed from a nearby supernova (6000 light years away). Chinese astronomers observed the event in the year 1054 and since that time the nebula has been expanding into what it appears like today. The Crab Pulsar is a neutron star at the center of the nebula and the remains of the original supernova.

How much work is done by the motor in a CD player to make a CD spin, starting from rest? The CD has a diameter of 12.0 cm and a mass of 15.8 g. The laser scans at a constant tangential velocity of 1.20 m/s. Assume that the music is first detected at a radius of 22.0 mm from the center of the disk. Use the tangential velocity of the the laser and the radius at which music is first detected to determine the angular velocity of the disc. Ignore the small circular hole at the CD’s center.

A cylinder of mass M=8 kg and radius R=20 cm slides down a frictionless hill from height H=10 m. At the bottom of the hill there is a plane with friction coefficient u=0.25. a) How far will the cylinder slide along the plane before it begins to roll smoothly? b) What will be the final speed of the center of mass of the cylinder? No friction 10 m Friction