An object with a mass of m = 5 kg is attached to the free end of a light string wrapped around a reel of radius r= 0.5 m and mass of M = 4.00 kg. The reel is a solid disk, free to rotate in a vertical plane about the horizontal axis passing through its center as shown in the figure below. The suspended object is released from rest. Find (a) the angular acceleration of spool, (b) the tension on the string, and (c)the angular speed of reel at 2.0 s.

A dragster starts from rest and accelerates down a track. Each tire has a radius of 0.320 m and rolls without slipping. At a distance of 418 m, the angular speed of the wheels is 255 rad/s. Determine (a) the linear speed of the dragster and (b) the magnitude of the angular acceleration of its wheels. (a) v = (b) a= i i

In the figure, two 5.40 kg blocks are connected by a massless string over a pulley of radius 2.40 cm and rotational inertia 7.40 × 10-4 kg-m². The string does not slip on the pulley; it is not known whether there is friction between the table and the sliding block; the pulley's axis is frictionless. When this system is released from rest, the pulley turns through 0.800 rad in 154 ms and the acceleration of the blocks is constant. What are (a) the magnitude of the pulley's angular acceleration, (b) the magnitude of either block's acceleration, (c) string tension T₁, and (d) string tension T₂? Assume free-fall acceleration to be equal to 9.81 m/s². (a) Number i (b) Number (c) Number i (d) Number i Units Units Units Units

A uniform disk of radius 0.489 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 0.211 N applied at the rim causes an angular acceleration of 0.115 rad/s2. Find the mass of the disk.