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Chapter 13 Rotation of a Rigid Body

Chapter 13 Rotation of a Rigid Body. 13.1 Rotational kinematics 13.2 Center of mass 13.3 Torque 13.4 Rotational dynamics 13.5 Rotation about a fixed axis 13.6 *Rigid-body equilibrium 13.7 Rotational energy.

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Chapter 13 Rotation of a Rigid Body

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  1. Chapter 13 Rotation of a Rigid Body 13.1 Rotational kinematics 13.2 Center of mass 13.3 Torque 13.4 Rotational dynamics 13.5 Rotation about a fixed axis 13.6 *Rigid-body equilibrium 13.7 Rotational energy

  2. Stop to think 13.1 page 373Stop to think 13.2 page 379Stop to think 13.3 page 383Stop to think 13.5 page 391 • Example 13.2 page 373 • Example 13.6 page 380 • Example 13.9 page 384 • Example 13.14 page 391 • Example 13.15 page 396 • The great Downhill Race Page 395

  3. Angular velocity and angular acceleration • Angular velocity • The sign convention is that ù is positive for counterclockwise (ccw) rotation, negative for clockwise (cw) rotation. • Angular acceleration Here á is angular acceleration

  4. Angular velocity and acceleration • Question: • What is the angular speed of ladybug1and 2 • What is the ratio of linear speed of ladybug2 to ladybug1 • What is the ratio of the centripetal • acceleration of ladybug2 to ladybug1

  5. The sign of angular velocity and acceleration

  6. The center of mass

  7. Torque • The ability of a force to cause a rotation depends on three factors • (1) the magnitude F of the force • (2) the distance r from the point of application to the pivot • (3) The angle at which the force is applied

  8. Quick quiz: The rods all have the same length and are pivoted at the dot. Rank in order, From largest to smallest, the five torques.

  9. Rotational Dynamics

  10. Rank in order, from largest to smallest , the angular acceleration áa to áe

  11. Moment of Inertial In general case: For a continuum mass object, sum becomes integral: Rotation about a Fixed Axis

  12. Rigid-body Equilibrium • For a rigid body in total equilibrium, there is no net torque, about any point • Pick any point you wish as a pivot point. The Net torque about this point is zero

  13. A student holds a meter stick straight out with one or more masses dangling from it. Rank in order, from most difficult to least difficult, how hard it will be for the student to keep the meter stick from rotating C > d > a = b

  14. Rotational energy • The object’s rotational energy is:

  15. The speed of a rotating rod

  16. Rolling motion

  17. Kinetic energy of a rolling object • K = K(rotation) + K(cm)

  18. The Great Downhill Race

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