Rotational Mechanics - 4

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Session
Rotational Mechanics - 4
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Session Objective

1. Angular Momentum of a Particle
2. Conservation of angular momentum
3. Angular Impulse

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Angular Momentum
Angular momentum of a particle
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Angular Momentum for a System of Particles
For a system of particles (i 1 to n)
Angular momentum depends on the position of the
axis
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Angular Momentum for a Rigid Body
For a rigid body
( I moment of inertia around the axis of
rotation)
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Conservation of Angular Momentum
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Conservation of Angular Momentum
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Equilibrium of a Rigid Body
Two conditions are necessary.

• Total force acting on the body
• must add up to zero (equilibrium of
• linear motion)

• Total torque acting on the body
• must add up to zero (equilibrium of
• rotational motion)

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Comparison
LINEAR ANGULAR
Mass
Momentum
Newtons Second Law
Work
Kinetic Energy
Power(constant force)
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Class Exercise - 1
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Solution
Kinetic energy at any point
Hence, answer is (a).
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Class Exercise - 2
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Solution
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Solution contd..
L is conserved
Hence, answer is (a).
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Class Exercise - 3
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Solution
L ( mvyr) is zero when vy 0
Hence, the answer is (c).
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Class Exercise - 4
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Solution
Hence, answer is (c).
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Class Exercise - 5
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Solution
Let the motion of P be in xy plane.z 0
Then y b is constant.
Hence, answer is (b).
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Class Exercise - 6
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Solution
I always has the form kmR2, where k is a fraction
or unity.
KE (rotatory) KE (translatory) if k 1 or I
mR2. This is true for a ring.
Hence, answer is (d).
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Class Exercise - 7
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Solution
Linear speed v of both wheels is the same.
Hence, answer is (a).
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Class Exercise - 8
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Solution
IA IB mARA2 mBRB2
mARA2 4mA(2RA)2
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Hence, answer is (d).
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Class Exercise - 9
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Solution
Hence, answer is (c).
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