In the figure, a solid cylinder of radius 17 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 = 26°. (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 = 6.0 m. How far horizontally from the roof's edge does the cylinder hit the level ground? (a) Number (b) Number i Units Units

Most gasoline engines in today's automobiles are belt driven. This means that the crankshaft, a rod which rotates and drives the pistons, is timed to the camshaft, the mechanism which actuates the valves, by means of a belt. Starting from rest, assume it takes t = 0.0100 s for a crankshaft with a radius of r₁ = 3.75 cm to reach 1550 rpm. If the belt does not stretch or slip, calculate the angular acceleration a2 of the larger camshaft, which has a radius of r2 = 7.50 cm, during this time period. α₂ = rad/s²

A wheel 2.10 m in diameter lies in a vertical plane and rotates about its central axis with a constant angular acceleration of 3.50 rad/s. The wheel starts at rest at t = 0, and the radius vector of a certain point P on the rim makes an angle of 57.3° with the horizontal at this time. At t = 2.00 s, find the following. (a) the angular speed of the wheel 7 rad/s (b) the tangential speed of the point P 7.35 m/s (c) the total acceleration of the point P m/s? magnitude 51.45 direction 4.086 ° with respect to the radius to point P (d) the angular position of the point P 8 Your response differs from the correct answer by more than 100%. rad Need Help? Read It Master It

A flywheel has a constant angular deceleration of 1.6 rad/s/s. If the flywheel comes to rest from an angular velocity of 269.2 rad/s, what was the angular displacement and the time for the wheel's rotation?

A centrifuge rotor is accelerated for 23. s from 8000 rpm to 13000 rpm (revolutions per minute). (a) What is its average angular acceleration? (b) Through how many revolutions has the centrifuge rotor turned during its acceleration period, assuming constant angular acceleration?

A person is riding a bicycle, and its wheels have an angular velocity of 16.1 rad/s. Then, the brakes are applied and the bike is brought to a uniform stop. During braking, the angular displacement of each wheel is 12.7 revolutions. (a) How much time does it take for the bike to come to rest? (b) What is the anguar acceleration (in rad/s2) of each wheel?

A Texas cockroach walks from the center of a circular disk (that rotates like a merry-go-round without external torques) out to the edge at radius R. The angular speed of the cockroach–disk system for the walk is (va = 5.0 rad/s and vb = 6.0 rad/s). After reaching R, what fraction of the rotational inertia of the disk does the cockroach have?

A disk, with a radius of 0.25 m, is to be rotated like a merry-go-round through 1000 rad, starting from rest, gaining angular speed at the constant rate aj through the first 500 rad and then losing angular speed at the constant rate -aj until it is again at rest. The magnitude of the centripetal acceleration of any portion of the disk is not to exceed 100 m/s?. (a) What is the least time required for the rotation? (b) What is the corresponding value of a1? (a) Number i Units (b) Number i Units

A cylinder 32.6 cm in diameter is at rest initially. It is then given an angular acceleration of 14.5 rad/s^2. Find the tangential speed of the outer edge of the cylinder at 6.08 s. Give your answer in m/s.

A solid cylinder with a mass of (5 kg) and a radius of (0.2 m) (I =12MR2) is initially rolling along a flat plane with a linear velocity of (10ms). The cylinder then comes to the edge of a ramp that is inclined by (34degrees) to the horizontal and begins to roll up the ramp. How high above the flat plane does the cylinder reach before it starts to roll back down?