Rolling Motion of a Rigid Object

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Rolling Motion of a Rigid Object

• AP Physics C
• Mrs. Coyle

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For pure rolling motion there is rolling without
slipping, so at point P vp 0.

• All points instantaneously rotate about the
  point of contact between the object and the
  surface (P).

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vp 2 vcm
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Rolling Motion
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Speed and Acceleration of the CM of a Rolling
Object

• vcm ?R
• acm a R

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Red Line Path of a particle on a rolling
object (cycloid)

• Green line Path of the center of mass of
  the rolling object

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http//cnx.org/content/m14374/latest/
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Rolling Motion a combination of pure translation
and pure rotation.
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The Total Kinetic Energy of a Rolling Object is
the sum of the rotational and the translational
kinetic energy.

• K ½ ICM ?2 ½ MvCM2

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Note

• Rolling is possible when there is friction
  between the surface and the rolling object.
• The frictional force provides the torque to
  rotate the object.

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Ex Accelerated Rolling Motion

• Ki Ui Kf U f
• Mgh ½ ICM ?2 ½ MvCM2
• vcm ?R
• There is no frictional work. Why not?
• Does friction cause a displacement at its
  point of action?

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Ex 52

• A bowling ball (on a horizontal surface) has a
  mass M, radius R, and a moment of inertia of
  (2/5)MR2 . If it starts from rest, how much work
  must be done on it to set it rolling without
  slipping at a linear speed v? Express the work in
  terms of M and v.Ans (7/10)Mv2

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Ex 54

• A uniform solid disk and a uniform hoop are
  placed side by side at the top of an incline of
  height h. If they are released from rest and roll
  without slipping, which object reaches the bottom
  first? Verify your answer by calculating their
  speeds when they reach the bottom in terms of h.
• Ans The disk, vdisk (4gh/3)1/2 , vring (gh)1/2