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## Chapter 12 Rotation of a Rigid Body

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**Chapter 12 Rotation of a Rigid Body**12.1 Rotational Motion 12.2 Center of Mass 12.3 Rotational energy 12.4 Moment of Inertia 12.5 Torque 12.6 Rotational dynamics 12.7 Rotation about a fixed axis 12.8 *Rigid-body equilibrium 12.9 Rolling Motion**Stop to think 12.1 page 342Stop to think 12.2 page 350Stop**to think 12.3 page 353Stop to think 12.4 page 357Stop to think 12.5 page 364 • Example 12.2 page 343 • Example 12.5 page 348 • Example 12.7 page 349 • Example 12.14 page 359 • Example 12.16 page 361 • The great Downhill Race Page 395**Angular velocity and angular acceleration**• Angular velocity • The sign convention is that ω is positive for counterclockwise (ccw) rotation, negative for clockwise (cw) rotation. • Angular acceleration Here α is angular acceleration**Angular velocity and acceleration**• Question: • What is the angular speed of ladybug1 • What is the ratio of linear speed of ladybug2 to ladybug1 • What is the ratio of the centripetal • acceleration of ladybug2 to ladybug1**A 500 g ball and a 2.0 kg ball are connected by a massless**50 cm-long rod. Where is the center of mass**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**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.**Rotational energy**• The object’s rotational energy is:**Moment of Inertial**In general case: For a continuum mass object, sum becomes integral: Rotation about a Fixed Axis**Static Equilibrium**• An object in total equilibrium has no net force and no net torque**Kinetic energy of a rolling object**• K = K(rotation) + K(cm)