1. Chapter 8: Rotational Motion Christopher Chui Chapter 8: Rotational Motion - Christopher Chui

2. Rotational Motion: Angular Quantities • A rigid body does not change shape, so that every particle stays in fixed positions relative to one another • Rotational motion implies all points in the body move in circles; the centers of these circles all lie on the axis of rotation • q in radians = L/r; 1 rad = 57.3o • Average angular velocity = w = Dq / Dt • Linear velocity = v = DL / Dt = r Dw / Dt = r w • Tangential acceleration = atan = r a • Centripetal acceleration = aR = v2/r = (r w)2/r = w2 r • Frequency = f = w / 2p or w = 2pf • 1 Hertz = 1 revolution/second; period T = 1/f Chapter 8: Rotational Motion - Christopher Chui

3. Comparing Angular vs Linear Motion • Angular Linear • w = wo + a t v = vo + at • w = wot + ½ a t2 x = vo t + ½ at2 • w2 = wo2 + 2 aq v2 = vo2 + 2ax • Average w = (w + wo)/2 average v = (v + vo)/2 Chapter 8: Rotational Motion - Christopher Chui

4. Torque • Torque = moment of force about the axis = rF • Torque = t = rF sin q • F = ma = mr a • t = mr2a for one particle = (rotational inertia) a • Moment of inertia = I = S mr2 (refer to page 223) • Newton’s 2nd law for rotation = S t = Ia = DL / Dt • The total angular momentum of a rotating body remains constant if the net torque acting on it is zero, Iw = Iowo = constant • Work done by torque, W = tDq Chapter 8: Rotational Motion - Christopher Chui

5. Problem Solving for Rotational Motion • Draw a clear and complete diagram • Draw a free body diagram showing all forces acting on the body • Identify the axis of rotation and calculate the torque about it • Apply Newton’s 2nd law for rotation, St = Ia • Solve the resulting equations for the unknowns • Estimate to see whether the answer is reasonable Chapter 8: Rotational Motion - Christopher Chui

6. Rotational Kinetic Energy • Rotational KE = ½ Iw2 • Total KE = ½ MvCM2 + ½ ICMw2 • Angular momentum = L = Iw • Newton’s 2nd law for rotation = St = Ia = DL /Dt • Conservation of angular momentum: The total angular momentum of a rotating body remains constant if the net torque acting on it is zero • Iw = Io wo = constant Chapter 8: Rotational Motion - Christopher Chui