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Figure 18 - Relation between angular velocity and linear velocity.

An­gular velocity times radius gives linear velocity

Relation of Torque to Angular Ac­celeration.— In order to produce linear acceleration, it is necessary to apply a force to the body, and the greater the force the greater the acceleration. To produce angular acceleration, it is necessary to applya torque to the body. The greater the torque, the greater is the angular acceleration that is pro­duced. For a particular body rotating about a fixed axis, it is found that the angular acceleration is proportional to the torque that produ­ces it. This factor of proportionality by which the angular acceleration must be multiplied in order to give the torque is a measure of the opposition of the body to being set in rotation. It is analogous to the mass of a body, which is a measure of the opposition of a body to being set in translation. The relation between the torque and the angular acceleration can be expressed by the equation

T = IA

where A = the angular acceleration in radians per second per second; T = the torque (force in poundals and distance in feet, or force in dynes and distance in centimeters); I = the factor of proportionality called the rotary inertia.

This relation is known as Newton’s second law for rotary motions. It states that the angular acceleration is proportional to the torque.

Rotary Inertia.— Experiment has shown that the opposition of a body to being set in translation is proportional to the mass of the body and does not depend on anything else. It is found, however, that the opposition which a body offers to being set in rotation, or accel­erated, about a fixed axis depends not only on the mass but also on the way in which this mass is distributed about the axis. This opposi­tion which is called the rotary inertia, or the moment of inertia, is proportional to the mass and to the square of the distance of the mass from the axis of rotation. For this reason, when it is desired to make the rotary inertia of a flywheel of given mass as large as possible, the mass of the wheel is concentrated in the rim. When the mass is con­centrated near the axis, the tendency of the wheel to continue in mo­tion, or its resistance to being set in motion, is much less. In order to calculate the rotary inertia, multiply each element of mass by the square of its distance from the axis of rotation, and then add together all these products [2, С. 54 - 55].

Read the text, translate it and answer the questions: In what way can we find the acceleration when acting force is variable? What is SHM? What is periodic motion? What is oscillatory motion? What is the period of the motion?

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