WJEC Physics for A2: Study and Rev Guide

3.1.2 Angular velocity The angular velocity , w , of a point moving at a constant rate in a circular path with its centre at point O is de ned as: w = angle swept out (about O) time taken , that is w = q t UNIT: rad s −1 For one whole revolution, q = 2 p , and t = T , the period of rotation, this being the time for one revolution (one cycle). Thus, w = 2 p T that is w = 2 p × 1 T so w = 2 p f , in which f is the frequency of rotation : the number of revolutions, or cycles, per unit time. Example Calculate the angular velocity of the seconds hand of a clock. Answer w = 2 p T = 2 p 60 s = 0.105 rad s −1 Scalar or vector? In advanced work, w is treated as a sort of vector (pointing along the rotation axis), allowing the handling of rotations about axes at various angles. At A-level we deal only with one axis direction in any problem, so we can treat w as a scalar. Speed and angular velocity Suppose a body moves round a circular path at speed v . It traverses an arc of length s = vt in a time t . But s = r q , so r q = vt , that is q t = v r . So w = v r and v = r w . O θ Fig. 3.1.2 Angle swept out s = vt θ = r θ v r O Fig. 3.1.3 Two expressions for s Angular velocity w w = angle swept out time taken = q t UNIT: rad s −1 The period of rotation , T , is the time for one revolution. UNIT: s The frequency , f , is the number of revolutions per unit time. UNIT: s −1 = hertz (Hz) T = 1 f = 2 p w ; f = 1 T = w 2 p Key Terms D A wheel of diameter 0.48m rotates at 3000 turns per minute. Determine (in SI units): a) its rotation frequency b) its angular velocity c) the speed of a point on its circumference. QUICKFIR QUICKFIRE QUICKFIRE 9 3.1 Circular motion