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?

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.

Consider a sphere of radius R and mass M rolling without slipping. Which form of kineticenergy is larger, translational or rotational?
Translational kineticenergy is larger.
Rotationalkineticenergy is larger.
Both are equal.
You need to know the speed of the sphere to tell.

A helicopter has two blades (see figure), each of which has a mass of 220 kg and can be approximated as a thin rod of length 6.7 m. The blades are rotating at an angular speed of 55 rad/s. (a) What is the total moment of inertia of the two blades about the axis of rotation? (b) Determine the rotationalkineticenergy of the spin

A 15 kg uniform disk of radius R = 0.25 m has a string wrapped around it, and a m = 5 kg weight is hanging on the string. The system of the weight and disk are initially at rest. When the 5 kg weight is released, it moves down and the disk rotates.
Consider the point when the 5 kg weight is moving with a speed of 1.3 m/s.

See attached file for proper format.
A and B are two separate clutch plates. Plate A has a mass of 36 kg, a
radius of gyration of 0.12 m and rotates at 660 rev min-1. Plate B has a
mass of 45 kg, a radius of gyration of 0.16 m and is stationary.
When the clutch plates are engaged, slipping ceases after 0.4 seconds and
t

A uniform ball with a mass of 125 g is rolling without slipping along the horizontal surface of a table with a speed of 4.50 m/s when it rolls off the edge and it falls towards the floor, 1.10 m below. What is the rotationalkineticenergy of the ball just before it hits the floor?
0.506 J
0.732 J
1.05 J

(a) Calculate the kineticenergy that the earth has because of its rotation about its own axis. Assume that the earth is a uniform sphere and that its path around the sun is circular. For comparison, the total energy used in the United States in one year is about 9.33 109 J.
(b) Calculate the kineticenergy that the earth ha

A belt drives a pulley of radius 4.0 cm and negligible mass as shown.
The pulley is attached to a larger, solid wheel of mass 60 kg and radius 30 cm that is initially at rest. The tension T1 in the belt is 150.0 N and the tension T2 is 50 N. What is the total, net torque on the pulley? What is the moment of inertia of the whe

A helicopter has 3 blades, each of them are 5.20m long and has a mass of 220kg.(each blade has a mass of 220kg, not the sum of the 3) The rotor is rotating at 385 rev/min.
a)What is the rotational inertia of the rotor assembly about the axis of rotation? (Each blade can be considered to be a thin rod rotated about one
end.)