|A disk with moment of inertia I1 rotates about a frictionless, vertical axle with angular speed Wi. A second disk, this one having moment of inertia I2 and initially not rotating, drops onto the first disk (see figure below). Because of friction between the surfaces, the two eventually reach the same angular speed wf. (a) Calculate wf. (b) Calculate the ratio of the final to the initial rotational energy. Before After

A bowler uses a lane with a coefficient of kinetic friction of 0.156. The bowler releases her 5.30 kg bowling ball with a translational speed of 3.45 m/s. At the moment of release, the ball is not rotating. As the ball slides, it begins to rotate. What is the work ?ncWnc done by friction on the ball before it transitions to rolling without slipping? Use g=9.81 m/s2 for the acceleration due to gravity.

A top has a rotational inertial of 0.0035 kgm2 and is spinning at a frequency of 68 rpm.  Determine the rotational kinetic energy of the top.  Express your answer in mJ.

Energy of a Bullet Dissipated by Plywood. As part of a criminal investigation, you need to determine how much of a bullet's energy is dissipated by a 0.500-inch piece of plywood. You construct a device that consists of three disks that are separated by a distance d = 0.850 m and rotate on a common axis. The bullet is fired through the first disk (a few inches above its center), which is composed of a light plastic that has a negligible effect on the speed of the bullet. The bullet then passes through the second disk, which is composed of 0.500-inch plywood. Finally, the bullet strikes the third disk, where it becomes embedded. The disks rotate with an angular velocity of w = 86.0 rad/s. The angular displacement between holes in the first and second disks is A012 = 0.269 rad, and the angular displacement between the holes in the second and third disks is A023 = 0.286 rad. If the mass of the bullet is 12.0 g, find (a) the initial speed of the bullet and (b) the energy dissipated by the…

When your new Peloton bike indicates that you are burning the maximum number of calories, the chain has a speed of v = 2.30 m/s. When the sprocket of radius r = 0.02 m is in contact with the chain it goes around the sprocket in a circular manner. (a) If the moment of inertia of the sprocket is 4.32 kgm2, what is the rotational kinetic energy of the sprocket?  (b) What is the centripetal acceleration of the chain as it makes contact with the sprocket?  (c) Given that the torque on the sprocket is 3.24 Nm what is the angular acceleration of the sprocket?  (d) Find the tangential acceleration of the sprocket.  (e) What is the total acceleration of the sprocket?

A light rope is wrapped several times around a large wheel with a radius of 0.400 m. The wheel rotates in frictionless bearings about a stationary horizontal axis, as shown in the figure below. The free end of the rope is tied to a suitcase with a mass of 15.0 kg. The suitcase is released from rest at a height of 4.00 m above the ground. The suitcase has a speed of 3.50 m/s when it reaches the ground. Calculate: What is the linear acceleration of the suitcase as it falls?  (Hint:  It’s not in free fall!) What is the resulting angular acceleration of the wheel? What is the angular velocity of the wheel when the suitcase hits the ground? What is the tension in the string as the suitcase falls?  (Hint: It is not equal to the weight of the case!  Use Newton’s Second Law!) What is the torque caused by that tension? What is the moment of inertia of the wheel?

A plane with a wingspan of d = 16 m loses control in flight and begins to spiral in a circle around the cockpit while in a vertical dive. It completes one rotation every t = 3.1 s.

A solid spherical jewel rolls smoothly from rest down a ramp. The jewel descends a vertical height of 1.2m to reach the bottom of the ramp. What is the jewel's speed at the bottom of the ramp? Hint: This problem has nothing to do with elasticity as we did not formally cover that topic, and the inertia of a solid sphere is found by 2/5 m r2

A hollow sphere rolls without slipping down a ramp that is 3.5 m long. the ramp is inclined at an angle of 20˚ with the horizontal. Use the conservation of energy to find the speed of the sphere at the bottom of the slope if it starts from rest. ( I= 2/3 m R2 )

The 11 kg disk has an angular velocity of w = 20 rad/s. (Figure 1) Figure 400 mm 500 mm 200 mm- A B ⒸO 500 mm с P (N) 5 2 1 of 1 -t(s) Part A If the brake ABC is applied such that the magnitude of force P varies with time as shown, determine the time needed to stop the disk. The coefficient of kinetic friction at B is μ = 0.4. Neglect the thickness of the brake. Express your answer to three significant figures and include the appropriate units. t = 0 Submit Value μA Provide Feedback Request Answer Units ? Next >