A motor exerts torque on a carousel for it to attain a speed of 2.5 rev/s starting from rest in 3.5s. Find the work done by the motor if the carousel has a radius of 27m and a mass of 1.75 x 105kg. Consider the carousel to be a thin-walled cylinder rotating about its center.
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- A cord is wrapped around a pulley that is shaped like a disk of mass m and radius r. The cord's free end is connected to a block of mass M. The block starts from rest and then slides down an incline that makes an angle O with the horizontal as shown in the figure below. The coefficient of kinetic friction between the block and the incline is µu. (a) Use the concepts of energy to find an expression for the block's speed as a function of position, d, down the incline. (b) Find the magnitude of the acceleration of the block in terms of µ, m, M, g and O. m,r, MA merry-go-round has a mass of 1450 kgkg and a radius of 7.50 mm . How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.10 ss ? Assume it is a solid cylinder.The figure below shows a ball with mass m = 0.322 kg attached to the end of a thin rod with length L = 0.454 m and negligible mass. The other end of the rod is pivoted so that the ball can move in a vertical circle. The rod is held horizontally as shown and then given enough of a downward push to cause the ball to swing down and around and just reach the vertically up position, with zero speed there. (a) What initial speed must be given the ball so that it reaches the vertically upward position with zero speed? m/s (b) What then is its speed at the lowest point? m/s (c) What then is its speed at the point on the right level with the initial point? m/s
- A disk of mass 3.8 kg and radius 0.17 m starts at the bottom of a 25 degree incline. It'stranslational velocity is 16 m/s. How far along the incline does it roll before coming to astop?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 UnitsA disk of radius = 2.02 mm is attached to a high-speed drill at a dentist’s office and is turning at 96,185 rad/sec. Determine the tangential speed of a point on the outer edge of this disk. Use g=9.8
- An airplane propeller consists if three radial blades, each of length 1.9 m and a mass 5.1 kg. What is the kinetic energy of this propeller when rotating at 2200 rev/min? Assume that each blade is (approximately) a uniform rod.A 34 kg hoop of radius 1.3 m, initially rotating at 301 revolutions per minute, is brought smoothly to a stop in 20 s. What is the average power (in Watts) associated with the force that brings the hoop to a stop?Suppose you had a machine for 100% efficiently transferring kinetic energy of a rotating bicycle pedal to electrical energy. If the mass of a pedal is 200 g, (a) how fast must the pedal be moving to power a 17.00 W LED light? (b) what is the angular speed, in rpm, if the distance from the centre of the crank to the pedal is 16 cm?
- A car is designed to get its energy from a rotating flywheel (solid disk) with a radius of 2.00 m and a mass of 400 kg. Before a trip, the flywheel is attached to an electric motor, which brings the flywheel's rotational speed up to 4500 rev/min. (a) Find the kinetic energy stored in the flywheel. (b) If the flywheel is to supply energy to the car as would a 20.0-hp motor, find the length of time the car could run before the flywheel would have to be brought back up to speed.A particle with mass 0.025kg is attached to massless cord passing through a hole in the surface. The block is originally revolving at a distance of 0.30m from the hole with an angular speed of 1.75 rad/s. The cord is then pulled from below, shortening the radius of the circle to 0.15m What is the new angular speed? How much work was done in pulling the cord?