3. A pulley, suspended from the ceiling, has a mass of 4.50 kg and a radius of 30.0 cm. A string is wrapped around the pulley and has a 2.00-kg mass hanging, at rest, from one end. The bottom of the mass is h = 80.00-cm above the ground. What is the angular speed of the pulley when the hanging mass Solid reaches the ground? disk h m

A disk is initially rotating counterclockwise around a fixed axis with angular speed w0. Answer the questions below.  A. What is the net torque acting on the disk if the radius is 0.6 m? B. If the moment of inertia of the disk is 4kg ∙ m^2, what is the angular acceleration of the disk? C. If the initial angular velocity is 6 rad/s counterclockwise, what is the angular velocity after 10 seconds? D. What happens to the angular velocity of the disk over time? Sketch a graph!

Two tangential forces F1 = 25 N and F2 = 10 N are applied to the rim of a solid cylinder of radius R = 0.2 m. The cylinder starts to rotate from rest, and reaches angular speed of 50 rpm in 5 seconds. Find the mass of the cylinder.

A cylindrical shell (I = MR2), a solid cylinder (I =1/2 MR2), and a solid sphere (I =2/5 MR2) all having the same radius is made to roll on a frictionless ramp with an angle θ from the horizontal. Which of these objects will be the last to reach the bottom of the ramp, if they started to roll without slipping from the same height? a. cylindrical shellb. solid cylinderc. solid sphered. Not enough information is given

63. mmh A thin rod has a length of 0.25 m and rotates in a circle on a fric- tionless tabletop. The axis is perpendicular to the length of the rod at one of its ends. The rod has an angular velocity of 0.32 rad/s and a moment of inertia of 1.1 X 10-³ kg · m². A bug standing on the axis decides to crawl out to the other end of the rod. When the bug (mass = 4.2 x 10-3 kg) gets where it's going, what is the angular velocity of the rod?

7. You are asked to design a turntable that is 55.8 cm in diameter that has a kinetic energy of 0.250 J when it is turning at 45.0 rev/min. a. What must its moment of inertia be? b. If you make the turntable in the shape of a uniform solid disk, what mass would it have?

A circular disk has a rotational inertia of 1.4 kg.m? and a constant angular acceleration of 4.4 rad/s2. If it starts from rest the work done during the first 8.1 s by the net torque acting on it is:

6. A uniform disk turns at 3.3 rev/s around a frictionless central axis. A nonrotating rod is dropped onto the disk. The rod has the same mass as the disk and length equal to the diameter of the disk. The two objects then turn together at the same rate with the centers lined up vertically. What is the new angular velocity (in rad/s) and new angular frequency (in rev/s)?

A solid 0.5950 kg ball rolls without slipping down a track toward a vertical loop of radius ?=0.6550 m. What minimum translational speed ?min must the ball have when it is a height ?=1.008 m above the bottom of the loop in order to complete the loop without falling off the track? Assume that the radius of the ball itself is much smaller than the loop radius ?. Use ?=9.810 m/s2 for the acceleration due to gravity.

A rotating wheel requires 3.0 seconds to rotate through 233.0 radians. Its angular speed at the end of the 3.0-second interval is 98.0 rad/s.  Find: a. The angular speed at the beginning of the 3.0-second interval.  b. The constant angular acceleration of the wheel.