A block (mass-12 kg) is hanging from a massless cord that is wrapped around a pulley (moment of inertia-1.4 x 10³ kg-m²), as the figure shows. Initially the pulley is prevented from rotating and the block is stationary. Then, the pulley is allowed to rotate as the block falls. The cord does not slip relative to the pulley as the block falls. Assume that the radius of the cord around the pulley remains constant at a value of 0.038 m during the block's descent. Find (a) the angular acceleration of the pulley and (b) the tension in the cord. (a) Number (b) Number Units Units

A disk has a moment of inertia of 2.50 x 10² kg-m² and spins on a frictionless axis through its center at an initial angular speed of 22.2 rad/s. A ring, initially not rotating, of mass 0.250 kg and radius 0.200 m, is dropped vertically onto the disk and sticks so that the combination rotates about a common axis, through their centers. What is the new angular speed of the system? Note: Iring = MR². O 23.8 rad/s O 22.2 rad/s ) 15.9 rad/s 14.8 rad/s 55.5 rad/s

A student gives a steady push to a ball at the end of a massless, rigid rod for 1 s, causing the ball to rotate clockwise in a horizontal circle as shown below. The rod’s pivot is frictionless. Sketch a graph of the ball’s angular velocity as a function of time for the first 3 s of the ball’s motion. You won’t be able to include numbers on the vertical axis, but your graph should have the correct sign and the correct shape

Problem 2: A pulley consists of a large disk of radius R and a small disk of radius r that are welded together and mounted on a horizontal frictionless axle through their common centers. The moment of inertia of this pulley is I. A box containing a turkey of mass M is suspended from a rope wound around the large disk; a box containing a pumpkin of mass m is suspended from a rope wound around the small disk. The ropes do not slip on the disks. The system is released from rest and the turkey begins to descend, while the pumpkin is being lifted up. M P A Derive an expression for the magnitude of the angular acceleration a of the pulley, in terms of system parameters. Assume that a counterclockwise motion of the pulley is the positive direction. MgR+mgR MgR-mgr MgR-mgR a a = a = I+MR2+mr2 I+MR²+mr² I+MR²+mR? MgR+mgr MgR-mgR MgR+mgR a = a = I+MR2+mr²2 I+MR²+mr² I+MR²+mR? Submit I give up! Hint Feedback

A pulley with moment of inertia I = 0.75 kg-m² and radius R = 15 cm is mounted on a wall. A light string is wrapped around the pulley with a mass m = 2.0 kg attached to the end. The pulley rotates as the mass falls. Use Newton's second law to calculate the acceleration of the mass. Check that your formula gives the expected behavior when I →0. => To help get started, the free body diagrams m and the pulley is shown below. T m Write down Newton's second law for each diagram. Use (and explain) the relationship R a = RO TIL R T

A block (mass = 1.7 kg) is hanging from a massless cord that is wrapped around a pulley (moment of inertia = 1.6 x 10-3 kg·m2), as the figure shows. Initially the pulley is prevented from rotating and the block is stationary. Then, the pulley is allowed to rotate as the block falls. The cord does not slip relative to the pulley as the block falls. Assume that the radius of the cord around the pulley remains constant at a value of 0.042 m during the block's descent. Find (a) the angular acceleration of the pulley and (b) the tension in the cord.

A playground merry-go-round of radius R = 2.00 m has a moment of inertia I = 250 kg · m2 and is rotating at 10.0 rev/min about a frictionless, vertical axle. Facing the axle, a 25.0-kg child hops onto the merry-go-round and manages to sit down on the edge. What is the new angular speed of the merry-go-round?

A thin rod has a length of 0.900 m and rotates in a circle on a frictionless tabletop. The axis is perpendicular to the length of the rod at one of its ends. The rod has an angular velocity of 0.607 rad/s and a moment of inertia of 1.06 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 (whose mass is 5 x 10-3 kg) gets where it's going, what is the change in the angular velocity of the rod? Number i Units

A 0.45 kg tetherball is attached to a pole and rotating in a horizontal circle of radius r₁ = 1.4 m and is circling at angular speed = 1.42 rad/s. As the rope wraps around the pole the radius of the circle shortens and became r2 = 0.9 m, that decreases the moment of inertia of the rotating tetherball. What is the moment of inertia of the rotating ball before the rope is wrapped around the pole measured in kgm² (answer with 3 decimal places)?

A child jumps to the edge of a carousel, that is in the shape of a circular plate with a radius of 1.3 m and was rotating at an angular velocity of 1.2 s-1 before the chuld jumped on it. The weight of the carousels is 80 kg, the weight of the child is 22 kg. What is their angular velocity after the jump? Later, the child moves closer to the center of the carousel plate by 80 cm. What is the new angular velocity?