ROTATIONAL KINETIC ENERGY

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Session
Rotational Mechanics - 6
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Session Objective

1. Angular momentum of a body in rolling
2. Friction in rolling
3. Motion of rigid bodies on frictionless and
   frictional inclined/horizontal plane
4. Problem Solving

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Angular Momentum in Rolling
The angular momentum about point of contact (P)
is given by
LP mvcmr Icw (i)
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Friction in Forward Slipping
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Friction in Backward Slipping
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Friction in Rolling on an Inclined Plan
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Class Exercise - 1
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Solution
V2 gt V1
Applying conservation of energy in thecase of
pure rolling,
Hence, answer is (a).
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Class Exercise - 2
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Solution
a, c, d

• Velocity will be affected by
• Radius It changes the M.I.
• Density It changes the mass distribution
  and,hence, the M.I.
• Change in height It changes the total energy.

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Class Exercise - 3
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Solution
As the point of contact moves forward, the
friction will act in the backward direction.
Hence, answer is (c).
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Class Exercise - 4
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Solution
Acceleration will be lower than that ona smooth
plane, as in pure rolling
Hence, answer is (a).
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Class Exercise - 5
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Solution
Hence, answer is (c).
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Class Exercise - 6

• Which of the following statements is not
  true?
• The instantaneous speed of the point of contact
  of disc rolling perfectly on a rough horizontal
  plane is zero
• (b) The frictional force on the same body is zero
• (c) The instantaneous acceleration of the point
  of contact of the same body is zero
• (d) Work done against frictional force in the
  case of same body is not zero

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Solution
b, d
The answers are definition of rolling.
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Class Exercise - 7
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Solution
Hence, answer is (b).
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Class Exercise - 8
A ball is released on a rough horizontal plane
with a speed v0 so that it slides on the surface
without rolling. To what value should the speed
decrease so that it rolls without sliding?
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Solution
The moment the ball touches thesurface with
speed v0 to right,frictional force f acts to the
left.
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Solution contd..
Translation
Rotation
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Solution contd..
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Class Exercise - 9
A solid sphere (radius R, mass M) is given a
clockwise angular velocity w0 and lowered to a
flat horizontal surface with coefficient of
friction m with the sphere. The sphere first
slips on the surface. After time t the motion
changes to pure rolling without slipping. What is
the value of t and the value of velocity of
centre of mass at t?
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Solution
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Solution
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Class Exercise - 10
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Solution
Hence, answer is (a).
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