Chapter 13 Rotation of a Rigid Body

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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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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
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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

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The sign of angular velocity and acceleration
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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 Dynamics
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Rank in order, from largest to smallest , the
angular acceleration áa to áe
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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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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

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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 gt d gt a b
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Rotational energy

• The objects rotational energy is

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The speed of a rotating rod
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Rolling motion
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Kinetic energy of a rolling object

• K K(rotation) K(cm)