A certain gyroscope consists of a uniform disk with a 50 cm radius mounted at the center of an axle that is 11 cm long and of negligible mass.The axle is horizontal and supported at one end. If the spin rate is 1000 rev/min, what is the precession rate?

A uniform disk of radius 0.491 m and unknown mass is constrained to rotate about a perpendicular axis through its center. A ring with the same mass as the disk is attached around the disk's rim. A tangential force of 0.229 N applied at the rim causes an angular acceleration of 0.115 rad/s². Find the mass of the disk. mass of disk: 3.08 kg

A car is traveling at 20.0 m/s on tires with a diameter of 70.0 cm. The car slows down to a rest after traveling 300.0 m. If the tires rolled without slipping, what was the magnitude of the average angular acceleration of the tires during the time the car slowed to a rest?

A 1.756-kg sphere of radius 0.31 m is rotating about an axis through its center at 24.843 rev/s with the angular velocity in the +z direction.  A torque 11.573N∙m acts on the sphere about the center of the sphere in the +x direction.  What is the angular acceleration, in rad2/s, of the sphere? (Isphere = 2/5 MR2)

A uniform 3.7-kg cylinder can rotate about an axis through its center at O. The forces applied are: F1 = 4.5 N, F2 = 7.1 N, F3 = 5.8 N, and F4 = 3.8 N. Also, R1 = 11.1 cm and R3 = 6.2 cm. Find the magnitude and direction (+: counterclockwise; -: clockwise) of the angular acceleration of the cylinder.

A gyroscope flywheel of radius 2.76 cm is accelerated from rest at 14.0 rad/s2 until its angular speed is 1740 rev/min. (a) What is the tangential acceleration of a point on the rim of the flywheel during this spin-up process? (b) What is the radial acceleration of this point when the flywheel is spinning at full speed? (c) Through what distance does a point on the rim move during the spin-up?

A uniform disc of mass 3.0 kg and radius 25 cm is mounted on a fixed horizontal axle. A block with mass 1.8 kg hangs from a light cord that is wrapped around the rim of the disc. What is the angular acceleration of the disc?

A string holds and wraps around a solid cylinder (7-kg and R = 3-m). A person pulls the string vertically upward, so the cylinder’s center of gravity does not move and is suspended in midair for 3 second. Note that the rotational inertia of the cylinder about its axis is MR2/2, the tension in the string is 3-N. what is the net force on the cylinder in Newton?

A wheel’s angular acceleration is constant. Initially its angular velocity is zero. During the first 1.0-s time interval, it rotates through an angle of 90.0°. (a) Through what angle does it rotate during the next 1.0-s time interval? (b) Through what angle during the third 1.0-s time interval?