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

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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

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Angular velocity and angular acceleration

• Angular velocity
• The sign convention is that ? is positive for
  counterclockwise (ccw) rotation, negative for
  clockwise (cw) rotation.
• Angular acceleration

Here a is angular acceleration
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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

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The sign of angular velocity and acceleration
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The center of mass
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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
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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

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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.
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Rotational energy

• The objects rotational energy is

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Moment of Inertial
In general case
For a continuum mass object, sum becomes integral
Rotation about a Fixed Axis
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Rotational Dynamics
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The speed of a rotating rod
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Static Equilibrium

• An object in total equilibrium has no net force
  and no net torque

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Rolling motion
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Kinetic energy of a rolling object

• K K(rotation) K(cm)

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The Great Downhill Race(P366)