A merry-go-round has rotational inertia I as it spins on a frictionless axle with angular speed w; . A security guard with mass m stands a distance R from its center, as illustrated.

In the figure, three 0.10 kg particles have been glued to a rod of length L = 11 cm and negligible mass and can rotate around a perpendicular axis through point O at one end. How much work is required to change the rotational rate (a) from 0 to 20.0 rad/s, (b) from 20.0 rad/s to 40.0 rad/s, and (c) from 40.0 rad/s to 60.0 rad/s? (d) What is the slope of a plot of the assembly's kinetic energy (in joules) versus the square of its rotation rate (in radians-squared per second-squared)? Axis -P--P-- P- (a) Number i Units (b) Number i Units (c) Number i Units (d) Number i Units

A Yo-Yo is falling with the string firmly attached to a stationarypoint. If both disks together have a mass of 0.15 kg and radius 20 mm, find its acceleration with an axle radius of 7 mm.

Lx Gi A 325-kg merry-go-round with a radius of 1.50 m is spinning counterclockwise, as viewed from above, at 4.80 rad/s. A 35.0-kg child is hanging on tightly 1.25 m from the rotation axis. Her father applies friction to the outer rim to slow the merry-go-round to a stop in 5 s. Model the merry-go-round as a solid disk, and define counterclockwise as the positive direction of rotation. How much torque t must the child's father apply? 432 T = N-m Incorrect

A bicycle tire is spinning clockwise at 3.10 rad/s. During a time period At = 1.70 s, the tire is stopped and spun in the opposite (counterclockwise) direction, also at 3.10 rad/s. Calculate the change in the tire's angular velocity Aw and the tire's average angular acceleration av: (Indicate the direction with the signs of your answers.) HINT (a) the change in the tire's angular velocity Aw (in rad/s) rad/s (b) the tire's average angular acceleration a. (in rad/s2) 'av rad/s? Need Help? Read It Watch It

A bowler throws a bowling ball of radius R = 11 cm along a lane. The ball (the figure) slides on the lane with initial speed vcom.O friction between the ball and the lane is 0.29. The kinetic frictional force 7k acting on the ball causes a linear acceleration of the ball while producing a torque that causes an angular acceleration of = 8.4 m/s and initial angular speed wo 0. The coefficient of kinetic the ball. When speed vcom has decreased enough and angular speed p has increased enough, the ball stops sliding and then rolls smoothly. During the sliding, what are the ball's (a) linear acceleration and (b) angular acceleration? (c) How long does the ball slide? (d) How far does the ball slide? (e) What is the linear speed of the ball when smooth rolling begins? Note that the clockwise direction is taken as negative. Vcotm (a) Number Units (b) Number Units (c) Number Units (d) Number Units (e) Number Units

A uniform drawbridge must be held at a 37° angle abovethe horizontal to allow ships to pass underneath. The drawbridge weighs45,000 N and is 14.0 m long. A cable is connected 3.5 m from thehinge where the bridge pivots (measured along the bridge) and pullshorizontally on the bridge to hold it in place. What is the angular speed of the drawbridge as it becomes horizontal?

A bicycle tire is spinning clockwise at 2.20 rad/s. During a time period At = 2.50 s, the tire is stopped and spun in the opposite (counterclockwise) direction, also at 2.20 rad/s. Calculate the change in the tire's angular velocity Aw and the tire's average angular acceleration aay. (Indicate the direction with the signs of your answers.) HINT (a) the change in the tire's angular velocity Aw (in rad/s) rad/s (b) the tire's average angular acceleration a (in rad/s2) rad/s2

If the child applies 21.5 N tangentially to the edge for 25 seconds, what is the angular speed, average work, and power supplied by the child?

A turnable with a moment of interia of 0.012 kg m² rotates freely at 2.0 rad/s. A circular disk of mass 200 g and diameter 30 cm, and initially not råtating, slips down a spindle and land on the turnable. (A) Find the new angular speed. (B.) Whot is the change in kinetic energy?