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# Measurement of the moment of inertia of a flywheel

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❶They find applications in technologies such as atomic energy or semiconductors.   Many carmakers are now testing flywheel energy storage devices in their automobiles, such as the flywheel, or kinetic energy recovery system, shown in Figure A KERS kinetic energy recovery system flywheel used in cars. The rotational and translational quantities for kinetic energy and inertia are summarized in Table Six small washers are spaced 10 cm apart on a rod of negligible mass and 0. The mass of each washer is 20 g. The rod rotates about an axis located at 25 cm, as shown in Figure Six washers are spaced 10 cm apart on a rod of negligible mass and rotating about a vertical axis.

We can see the individual contributions to the moment of inertia. The masses close to the axis of rotation have a very small contribution.

When we removed them, it had a very small effect on the moment of inertia. In the next subsection, we generalize the summation equation for point particles and develop a method to calculate moments of inertia for rigid bodies.

For now, though, Figure Values of rotational inertia for common shapes of objects. The following examples will also help get you comfortable using these equations. A typical small rescue helicopter has four blades: The blades can be approximated as thin rods that rotate about one end of an axis perpendicular to their length. The helicopter has a total loaded mass of kg. Rotational and translational kinetic energies can be calculated from their definitions. The wording of the problem gives all the necessary constants to evaluate the expressions for the rotational and translational kinetic energies.

The ratio of translational energy to rotational kinetic energy is only 0. This ratio tells us that most of the kinetic energy of the helicopter is in its spinning blades. A person hurls a boomerang into the air with a velocity of It has a mass of 1.

We use the definitions of rotational and linear kinetic energy to find the total energy of the system. In part b , we use conservation of mechanical energy to find the maximum height of the boomerang. In part b , the solution demonstrates how energy conservation is an alternative method to solve a problem that normally would be solved using kinematics. In the absence of air resistance, the rotational kinetic energy was not a factor in the solution for the maximum height.

A nuclear submarine propeller has a moment of inertia of If the submerged propeller has a rotation rate of 4. Skills to Develop Describe the differences between rotational and translational kinetic energy Define the physical concept of moment of inertia in terms of the mass distribution from the rotational axis Explain how the moment of inertia of rigid bodies affects their rotational kinetic energy Use conservation of mechanical energy to analyze systems undergoing both rotation and translation Calculate the angular velocity of a rotating system when there are energy losses due to nonconservative forces.

Rotational Kinetic Energy Any moving object has kinetic energy. Zachary David Bell, US Navy Energy in rotational motion is not a new form of energy; rather, it is the energy associated with rotational motion, the same as kinetic energy in translational motion. Moment of Inertia If we compare Equation Strategy We use the definition for moment of inertia for a system of particles and perform the summation to evaluate this quantity.

The masses are all the same so we can pull that quantity in front of the summation symbol. We do a similar calculation. We insert the result from a into the expression for rotational kinetic energy. Significance We can see the individual contributions to the moment of inertia. Rotational Energy Determine that energy or work is involved in the rotation. Determine the system of interest. A sketch usually helps. Analyze the situation to determine the types of work and energy involved.

Because light is an electromagnetic wave, other forms of electromagnetic radiation such as X-rays, microwaves, and radio waves exhibit similar properties. Resolving power of a prism Angle of the prism using Spectrometer Spectrometer i-i' curve Spectrometer: This part Includes theoretical description of crystal and electronic structure, lattice dynamics, and optical properties of different materials.

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The flywheel consists of a heavy circular disc or wheel with a strong axle mounted on ball bearings on two fixed ladies.ml wheel can be rotated in a vertical plane about the horizontal ladies.ml is used to determine the moment of inertia.

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The moment of inertia of the flywheel and axle is I. The flywheel is accelerated by the couple applied by the mass m. The mass is allowed to fall through a height h at which point the string leaves the axle. The velocity of the falling mass at this instant is v and the angular velocity of the flywheel ω.