A wheel is rotating about an axis perpendicular to the plane of the wheel and passing through the center of the wheel. The angular speed of the wheel is increasing at a constant rate. Point A is on the rim of the wheel and point B is midway between the rim and center of the wheel. For each of the following quantities, is its magnitude larger at point A or at point B, or is it the same at both points? (a) angular speed; (b) tangential speed; (c) angular acceleration; (d) tangential acceleration; (e) radial acceleration. Justify each answer.

Solution 21DQ To solve this question, we shall have to take some relations in hand. v I. Angular speed = r , v is linear speed and r is the radius II. Tangential speed v = t , a III. Angular acceleration = r, a is tangential acceleration IV. Tangential acceleration a = t V. Radial acceleration a = r r 2 (a) The point A is far away from the axis of rotation, hence angular speed will be larger at the point B for its proximity to the axis of rotation. (I) (b) Here, point A is farther from the rotation axis than point B. So, tangential speed at A will be greater. (II) (c) Angular acceleration will be greater at B, since it is closer to rotation axis. (III) (d) Tangential acceleration will be greater at A as it is farther from the rotation axis than B. (IV) (e) Radial acceleration will also be greater at A. (V)