# Angular acceleration and rotational kinetic energy

Three objects are positioned along the x axis as follows: 4.4 kg at x = +1.1m, 3.7 kg at x = -0.80m, and 2.9 kg at x = -1.6 m. The acceleration due to gravity is the same everywhere. What is the distance from location of the center of gravity to the location of the center of mass for this system

A ceiling fan has five blades, each with a mass of 0.34 kg and a length of 0.66 m. The fan is operating in its "low" setting at which the angular speed is 9.4 rad/s. If the blades can be approximated as uniform thin rods that rotate about one end, what is the total rotational kinetic energy of the five blades?

A 50-kg rider on a moped of mass 75 kg is traveling with a speed of 20 m/s. Each of the two wheels of the moped has a radius of 0.2 m and a moment of inertia of 0.2 kg m. What is the total rotational kinetic energy of the wheels

During the spin dry cycle of a washing machine, the motor slows from 95 rad/s to 30 rad/s while the turning the drum through an angle of 402 radians. What is the magnitude of the angular acceleration of the motor?

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#### Solution Summary

The solution provides a theory explanation and then detailed and step-by-step calculations for the problem. The Word file is 3 page long.

Yo-yo speed and energy; angular speed of a bicycle wheel

A yo-yo has a rotational inertia of 1180 g·cm2 and a mass of 148 g. Its axle radius is 3.58 mm, and its string is 139 cm long. The yo-yo rolls from rest down to the end of the string. (a) What is the magnitude of its linear acceleration? (b) How long does it take to reach the end of the string? As it reaches the end of the string, what are its (c) linear speed, (d) translational kinetic energy, (e) rotational kinetic energy, and (f) angular speed?

With axle and spokes of negligible mass and a thin rim, a certain bicycle wheel has a radius of 0.350 m and weighs 36.0 N; it can turn on its axle with negligible friction. A man holds the wheel above his head with the axle vertical while he stands on a turntable that is free to rotate without friction; the wheel rotates clockwise, as seen from above, with an angular speed of 53.0 rad/s, and the turntable is initially at rest. The rotational inertia of wheel + man + turntable about the common axis of rotation is 2.50 kg·m2. The man's free hand suddenly stops the rotation of the wheel (relative to the turntable). (a) Determine the resulting angular speed of the system. (b) Is the direction of the rotation: 1 - clockwise or 2 - counterclockwise? Give the number of the correct answer.

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