A spool of thread consists of a cylinder of radius R1 = 7.2 cm with end caps of radius R2 = 9.0 cm as depicted in the end view shown in the figure below. The mass of the spool, including the thread, is m = 180 g. The spool is placed on a rough, horizontal surface so that it rolls without slipping when a force T 0.450 N acting to the right is applied to the free end of the thread. For the moment of inertia treat the spool as being a solid cylinder of radius R1, as the extended edges are thin and therefore light.

The outstretched hands and arms of a figure skater preparing for a spin can be considered a slender rod pivoting about an axis through its center ( Ibar=ml² where l is the length of the bar). When the skater's hands and arms are brought in and wrapped around their body to execute the spin, the hands and arms can be considered a thin-walled hollow cylinder. The hands and arms have a combined mass 10 kg. When outstretched, they span 2.1 m. When wrapped, they form a cylinder of radius 21 cm. The moment of inertia about the rotation axis of the remainder of the body is constant and equal to 0.6 kg-m2. If the original angular speed is 0.5 rev/s, what is the final angular speed? 00f= rev/s Determine how much the figure skater's rotational KE increased. [NOTE: We express energy in J. To get J, you must convert your angular velocities to the appropriate mks. units which are rad/s.] ΔΚΕ- =

Two wheels have the same mass and radius of 4.9kg and 0.45 m, respectively. One has (a) the shape of a hoop and the other (b) the shape of a solid disk. The wheels start from rest and have a constant angular acceleration with respect to a rotational axis that is perpendicular to the plane of the wheel at its center. Each turns through an angle of 13 rad in 8.4 s. Find the net external torque that acts on each wheel.

A solid cylinder with mass m, radius R, and rotational inertia I (about its center) is released from rest and rolls down a ramp.  Friction between the bottom of the cylinder and the ramp causes the cylinder to roll without slipping.  The linear acceleration of the cylinder is a.  Which TWO of the equations below are correct for this scenario? The equations are in terms of m, I, R, and a, as well as f (the force of static friction between the cylinder and the ramp) and g.  (You must pick BOTH of them to get this question correct!) f = ma mg sin θ = ma mg sin θ - f = ma f R = I (a/R) mg sin θ - f = I (a/R) R mg sin θ = IaR

A ceiling fan consists of a small cylindrical disk with 5 thin rods coming from the center. The disk has mass md = 2.7 kg and radius R = 0.25 m. The rods each have mass m, = 1.2 kg and length L = 0.86 m.

Question 16 my m, Two blocks are joined by a pulley system (see Figure). The pulley is a solid disk of mass 0.5 kg and radius 179 mm. Assume that the pulley rotates smoothly. If mass 1 is 4.4 kg and mass 2 is 15 kg, what is the angular acceleration of the disk? HINT: the tensions in the horizontal and vertical portions of the rope are not equal. (PUHQ1629)

A cylindrical metal drum, with a radius of 0.25 m, has an inertia of 11.0.kg. The drum is hollow and you may neglect the inertia of the top and bottom of the drum. The drum is free to rotate about an axle that runs through its centre and along its long axis. A cord is wrapped around the drum. The cord is pulled straight from the drum with a constant force of 60 N. As the cord unwinds, the drum rotates, with no slippage between the cord and the drum. (a) Calculate the work done by person pulling the cord as the drum rotates through 100 radians. Give your answer in Joules (b) Assuming the drum starts from rest, what is the rotational speed of the tyre after it has rotated through 100 radians? Give your answer in rad.s

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?

The uniform solid block in the figure has mass 39.8 kg and edge lengths a = 0.902 m, b = 1.67 m, and c = 0.141 m. Calculate its rotational inertia about an axis through one corner and perpendicular to the large faces. Number:   Unit:

A wheel consists of a rim (ring) with a mass of 1.3kg and a radius of 0.45m and four equally-spaced spokes (rods) that run from the center of the wheel to the edge of the rim. Each spoke has a mass of 0.15kg and a length equal to the radius of the wheel. What is the total rotational inertia of the wheel about its center?