Lecture 17: Angular momentum

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Lecture 17Angular momentum

• Phys 2101
• Gabriela González

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Newtons law systems of particles
total linear momentum
total angular momentum
No forces, no linear momentum conservation of
linear momentum. No torques, no angular momentum
conservation of angular momentum.
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Newtons law
No forces, no linear momentum conservation of
linear momentum. No torques, no angular momentum
conservation of angular momentum.
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Conservation of angular momentum
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Example

• A 4.0 kg particle moves in an xy plane. At the
  instant when the particle's position and velocity
  are r (2.0 i 4.0 j ) m and v -4.0 j m/s,
  the force on the particle is F -3.0 i N. At
  this instant, determine
• the particle's angular momentum about the origin,
• the particle's angular momentum about the point
  x 0, y 4.0 m,
• the torque acting on the particle about the
  origin, and
• the torque acting on the particle about the
  point x 0, y 4.0 m.

y
F
v
r
x
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Example

• A 30 kg child stands on the edge of a stationary
  merry-go-round of mass 100 kg and radius 2.0 m.
  The rotational inertia of the merry-go-round
  about its axis of rotation is 150 kgm2. The
  child catches a ball of mass 1.0 kg thrown by a
  friend. Just before the ball is caught, it has a
  horizontal velocity of 12 m/s that makes an angle
  of 37 with a line tangent to the outer edge of
  the merry-go-round, as shown in the overhead view
  of the figure. What is the angular speed of the
  merry-go-round just after the ball is caught?

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Example

• A 1.0 g bullet is fired into a 0.50 kg block that
  is mounted on the end of a 0.60 m nonuniform rod
  of mass 0.50 kg. The blockrodbullet system then
  rotates about a fixed axis at point A. The
  rotational inertia of the rod alone about A is
  0.060 kgm2. Assume the block is small enough to
  treat as a particle on the end of the rod.
• What is the rotational inertia of the
  blockrodbullet system about point A?
• If the angular speed of the system about A just
  after the bullet's impact is 4.5 rad/s, what is
  the speed of the bullet just before the impact?