A spool consists of a cylinder with two circular disks glued on either end. It has mass m, moment of inertia I, inner (cylinder) radius r, and outer (disk) radius R. String is wrapped tightly around the cylinder. The spool is placed on its side and the string is pulled with force T from an angle 0 above the horizontal. The spool rolls without slipping. (a) Compute the angular acceleration about the center of mass at the instant the force is first applied. (b) Which way does the spool roll, right or left? Does this depend on the properties of the spool and/or the angle 0? If so, find a formula. Note: if you did not succeed in part 1, you can still get partial credit here for a correct qualitative discussion.

While punting a football, a kicker rotates his leg about the hip joint. The moment of inertia of the leg is 3.34 kg · m2 and its rotational kinetic energy is 157 J. (Enter the magnitudes.) What is the angular velocity of the leg (in rad/s)? What is the velocity (in m/s) of the tip of the punter's shoe if it is 1.05 m from the hip joint?

A grindstone has a moment of inertia of 6 x 10-3 kg m2. When a constant torque is applied, the flywheel reaches an angular velocity of 1200 rev/min in 15 s. Assuming it started from rest, find the angular acceleration. Find the unbalanced torque applied. Find the angle turned through in the 15 s. Find the work W done on the flywheel by the torque.

In the figure, wheel A of radius -9.40 cm is coupled by belt B to wheel C of radius rc-26.1 cm. The angular speed of wheel A is increased from rest at a constant rate of 2.53 rad/s². Find the time needed for wheel C to reach an angular speed of 63.0 rev/min, assuming the belt does not slip. (Hint: If the belt does not slip, the linear speeds at the two rims must be equal.) Number Ma Units B

A turntable 46.0 cm in diameter diameter starts from rest, and rotates at 68.0 rpm at its first complete revoļution with constant angular acceleration. If it maintains the same acceleration, a) what is the rotational speed at time 34.0 seconds? b) what is the tangential speed of a point 10 cm from the edge of the turntable at time 34.0 seconds? Enter answer "O" in the answer box. Submit in the corresponding folder (or email) your solution by 3:50 pm, include a sketch/drawing of the rotating wheel, and a step- by-step solution.

In the figure, a solid cylinder of radius 16 cm and mass 16 kg starts from rest and rolls without slipping a distance L = 6.9 m down a roof that is inclined at angle 0 = 32°. (a) What is the angular speed of the cylinder about its center as it leaves the roof? (b) The roof's edge is at height H = 6.8 m. How far horizontally from the roof's edge does the cylinder hit the level ground? (a) Number i (b) Number IN Units Units 0 H

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.

In the figure, a solid cylinder of radius 5.5 cm and mass 14 kg starts from rest and rolls without slipping a distance L = 6.9 m down a roof that is inclined at angle = 39°. (a) What is the angular speed of the cylinder about its center as it leaves the roof? (b) The roof's edge is at height H = 5.2 m. How far horizontally from the roof's edge does the cylinder hit the level ground? (a) Number (b) Number i Units Units H

A flywheel with a diameter of 2.12 m is rotating at an angular speed of 92.5 rev/min. (a) What is the angular speed of the flywheel in radians per second? (b) What is the linear speed of a point on the rim of the flywheel? (c) What constant angular acceleration (in revolutions per minute-squared) will increase the wheel's angular speed to 1250 rev/min in 58.6 s? (d) How many revolutions does the wheel make during that 58.6 s?