1 / 6

Chapter 8: Rotational Motion

Chapter 8: Rotational Motion. Christopher Chui. Rotational Motion: Angular Quantities. A rigid body does not change shape, so that every particle stays in fixed positions relative to one another

janna-pierce
Télécharger la présentation

Chapter 8: Rotational Motion

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related