2.0 m 9.0 N 0.120 m 50 kg
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We wrap a light, nonstretching cable around a solid cylinder, of
mass 50 kg and diameter 0.120 m, that rotates in frictionless bearings
about a stationary horizontal axis (Fig.). We pull the free
end of the cable with a constant 9.0 N force for a distance of 2.0 m;
it turns the cylinder as it unwinds without slipping. The cylinder is
initially at rest. Find its final angular speed and the final speed of
the cable.
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- A playground merry-go-round has radius 2.40 m and moment of inertia 2100 kg . m2 about a vertical axle through its center, and it turns with negligible friction. (a) A child applies an 18.0 N force tangentially to the edge of the merry-go-round for 15.0 s. If the merrygo- round is initially at rest, what is its angular speed after this 15.0 s interval? (b) How much work did the child do on the merry-go-round? (c) What is the average power supplied by the child?You spin a disk, giving it an initial angular velocity of 2.50 rad/s clockwise. After you give it that initial spin, the disk has a constant angular acceleration of 0.400 rad/s? counterclockwise. (a) How much time passes before the disk reverses direction? (b) What is the disk's angular displacement, relative to its starting position, at the instant it comes instantaneously to rest? rad (c) At t = 12.0 s after you gave it its initial angular velocity, what is the disk's angular velocity? Use a positive sign for clockwise, and a negative sign for counterclockwise. rad/sA 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 top has a peg along its axis with a lightweight cord wrapped around it. As shown below, the end of the cord is pulled with a constant tension force F = 4.48 N, causing the cord to unwind from the peg without slipping. The top has a moment of inertia of 5.50 x 10-4 kg · m². It is initially at rest and is free to rotate about the stationary axis AA'. What is the top's angular speed (in rad/s) after 70.0 cm of cord has unwound from the peg? rad/sA playground merry-go-round of radius R = 1.80 m has a moment of inertia of 1 = 290 kgm² and is rotating at 14.0 rev/min about a frictionless vertical axis. Facing the axle, a 29.0 kg child hops on to the merry-go-round and manages to sit down on its edge. What is the new angular speed of the merry-go-round? O 1.11 rad/s 0.903 rad/s O 10.6 rad/s O4.53 rad/s practice q# 2 p. 242 chap 7You are trying to get a better feel for the effect of geometry and mass distribution on the moment of inertia. You have a solid disk and a thin ring, each of radius, r = 1.30 m, and mass, m = 73.0 kg. You mount both on fixed, horizontal frictionless axes about which they can spin freely. Then you spin them both. (a) How much work do you need to do to get each object to spin at 3.00 rad/s? (b) Let us assume that you have been causing them to spin by using a constant force applied tangentially to their circumferences. If the above speed is to be reached within 0.700 s, what is the magnitude of the force you need to apply to each object? (c) You next attempt to stop each object by pressing one finger on each side of each object, right at the outer edge. The coefficient of kinetic friction between each finger and the surface of each object is 0.300. Find the minimum force you have to apply to stop each object within 1.00 min.
- A solid uniform disk of diameter 3.20 m and mass 42 kg rolls without slipping to the bottom of a hill, starting from rest. If the angular speed of the disk is 4.27 rad/s at the bottom, how high did it start on the hill?Flywheels are large, massive wheels used to store energy. They can be spun up slowly, then the wheel’s energy can be released quickly to accomplish a task that demands high power. An industrial flywheel has a 1.5 m diameter and a mass of 250 kg. A motor spins up the flywheel with a constant torque of 50 N ⋅ m. How long does it take the flywheel to reach top angular speed of 1200 rpm?A ball with a weight of 70 N hangs from a string that is coiled around a 3 kg pulley with a radius of 0.4 m. Both the ball and the pulley are initially at rest. The rotational inertia of the pulley is 0.5mr2 and the ball is released from rest. Calculate the ball's velocity after it falls a distance of 2 meters.
- 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 HA uniform spherical shell of mass M = 11.0 kg and radius R = 0.810 m can rotate about a vertical axis on frictionless bearings (see the figure). A massless cord passes around the equator of the shell, over a pulley of rotational inertia I = 0.120 kg-m2 and radius r = 0.120 m, and is attached to a small object of mass m = 4.60 kg. There is no friction on the pulley's axle; the cord does not slip on the pulley. What is the speed of the object when it has fallen a distance 0.962 m after being released from rest? Use energy considerations. %3D М, R I,rA cylinder is rotating about an axis that passes through the center of each circular end piece. The cylinder has a radius of 0.110 m, an angular speed of 64.0 rad/s, and a moment of inertia of 1.08 kg-m². A brake shoe presses against the surface of the cylinder and applies a tangential frictional force to it. The frictional force reduces the angular speed of the cylinder by a factor of 9 during a time of 8.00 s. (a) Find the magnitude of the angular deceleration of the cylinder. (b) Find the magnitude of the force of friction applied by the brake shoe. (a) Number i (b) Number i Units Units