A uniform disk with radius R = 0.400 m and mass 30.0 kg rotates in a horizontal plane on a frictionless vertical axle that passes through the center of the disk. The angle through which the disk has turned varies with time according to θ(t) =(1.10 rad/s)t + (6.30 rad/s2)t2. What is the resultant linear acceleration of a point on the rim of the disk at the instant when the disk has turned through 0.100 rev?

A yo‑yo with a mass of 0.0850 kg and a rolling radius of r=1.60 cm rolls down a string with a linear acceleration of 5.20 m/s2. Calculate the tension magnitude ? in the string and the angular acceleration magnitude ? of the yo‑yo.

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 motor spins a disk (Idisk = 25.5 kg*m2) with a torque of 39 N*m, and a 18 N frictional force acts on the disk at a radius of 1.4 m. Attached to the disk at a radius of 6.6 m is a 13 kg mass. What is the magnitude of the angular acceleration in rad/s2 of the system?

A bicycle wheel, of radius 0.300 m and mass 1.59 kg (concentrated on the rim), is rotating at 4.00 rev/s. After 52.8 s the wheel comes to a stop because of friction. What is the magnitude of the average torque due to frictional forces?

A student holds a bike wheel and starts it spinning with an initial angular speed of 9.09.0 rotations per second. The wheel is subject to some friction, so it gradually slows down. In the 10.0 s10.0 s period following the inital spin, the bike wheel undergoes 65.065.0 complete rotations. Assuming the frictional torque remains constant, how much more time Δ?sΔ⁢ts will it take the bike wheel to come to a complete stop?   Δ?s=Δ⁢ts=   ss The bike wheel has a mass of 0.725 kg0.725 kg and a radius of 0.385 m0.385 m. If all the mass of the wheel is assumed to be located on the rim, find the magnitude of the frictional torque ?fτf that was acting on the spinning wheel.

= - = 6. A mass M₁ 10 kg resting on a horizontal frictionless surface is attached to a M₂ = 7 kg weight by a light wire that passes over a frictionless pulley. See figure. The pulley has the shape of a uniform disk of mass M3 4 kg and radius R 0.3 m. After the system is released, find (a) the tension in the wire on both sides of the pulley, (b) the acceleration of M₁, and (c) the horizontal and vertical forces that the axle exerts on the pulley. M1 M 3 M2

A motor spins a disk (Idisk = 25.1 kg*m2) with a torque of 40 N*m, and a 18 N frictional force acts on the disk at a radius of 1.5 m. Attached to the disk at a radius of 2.6 m is a 17 kg mass. What is the magnitude of the angular acceleration in rad/s2 of the system?

The radius of a wheel is 0.890 m. A rope is wound around the outer rim of the wheel. The rope is pulled with a force of magnitude 5.00 N, unwinding the rope and making the wheel spin CCW about its central axis. Ignore the mass of the rope. (a) What is the angular displacement Δθ, in radians, of the wheel during 1.10 revolution? ___rad