1 / 19

Chapter 10

Chapter 10. Rotation of a Rigid Object About a Fixed Axis. Rolling Motion. Rigid body—object or system of particles in which distances between component parts remains constant Translational motion—movement of the system as a whole Described by the motion of the center of mass

aderyn
Download Presentation

Chapter 10

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 10 Rotation of a Rigid Object About a Fixed Axis

  2. Rolling Motion • Rigid body—object or system of particles in which distances between component parts remains constant • Translational motion—movement of the system as a whole • Described by the motion of the center of mass • Rotational motion—movement of individual parts around a particular axis • The spinning

  3. Angular Measure • Circular system of position measurement • Useful when objects move in circular (or partially circular) paths • Planetary motion (orbits) • Useful when objects are rotating • Planetary motion (rotation)

  4. Angular measure • Rectangular (Cartesian) coordinates • x—perpendicular distance from the vertical axis • y—perpendicular distance from the horizontal axis • Angular (circular) coordinates • If a line is drawn directly from the origin to any point . . . • r—distance from the origin • --angle made with the horizontal • Units of degrees or radians • x = rcos • y = rsin

  5. Angular measure • Displacement • x or y = linear displacement •  = angular displacement • For a circle • r = 0, so only angular displacement is needed to describe motion

  6. Angular measure • Radians • s = arclength • Distance around a circular path • 1 radian = angle that produces an arclength equal to r • 1 rad = 57.3 • Degrees • 1 revolution = 360 = 2 rad • 1 = 60 minutes • 1 minute = 60 seconds • *parsec

  7. Angular measure • Angular speed () • Units of rad/s • rpm—revolutions per minute • Common unit, but not standard metric • Angular velocity () • Direction given by right hand rule • Curl fingers in direction of rotation () • Thumb points in direction of 

  8. Angular measure • Instantaneous linear velocity (v) is in a straight line tangent to the circular path • v = r • For constant angular velocity, tangential (linear) velocity increases with the distance from the origin • How CD’s work

  9. Angular measure • Period (T)—time required for 1 complete revolution (cycle) • Units of seconds (s) • Frequency (f)—number of revolutions completed every second • Units of 1/s, s-1, cycles/s • Renamed Hertz (Hz)

  10. Angular Kinematics • Angular acceleration () = rate of change of angular velocity • Does not apply to Uniform Circular Motion • Related to linear (tangential) acceleration Example 7.10, p. 225

  11. Angular Kinematics • Angular Kinematic Equations

  12. Rolling motion • Rolling without slipping—surface do not move with respect to the point of contact • Direct relationship between rotational and translational motion • s = distance traveled by the center of mass • vcm = velocity of the center of mass • acm = acceleration of the center of mass

  13. Torque • Force is the cause of translational acceleration • Torque() is the cause of rotational acceleration • Units of m*N or N*m (not Joules) • The meter-Newton or Newton-meter • Moment arm (r)—distance from the axis of rotation to the the point where force is applied • Only component of force perpendicular to moment arm contributes to rotation Muscle Torque

  14. Equilibrium • Translational equilibrium • F = 0 • No net force • Rotational equilibrium •  = 0 • No net torque • Static Equilibrium—no movement • Kinetic Equilibrium—constant velocity See-saw Meter stick, page 258

  15. Rotational Dynamics • Newton’s 2nd Law (translational) • F = mass x acceleration • Newton’s 2nd Law (rotational) •  = rotational equivalent of mass x rotational equivalent of acceleration

  16. Rotational Dynamics • I = moment of inertia • Rotational equivalent of mass • Distribution of mass • Dependent on axis of rotation common geometrical shapes, p. 304

  17. Moment of Inertia

  18. Moment of Inertia

  19. Rotational Kinetic Energy • Remember, all your translational equations have rotational equivalents • Rotational work • Rotational KE • Rotational Work-Energy Theorem

More Related