8. In the figure, two platters are free to rotate without friction around the axis of rotation through their centers. Main platter with radius R1 = 30 cm is rotating with a constant angular velocity of w1 = 5 rad/s in counterclockwise direction. The second platter with radius R2 = 20 cm is rotating with a constant angular velocity of wz = 20 rad/s in the opposite direction above the platter M1. After a time, the platter M2 drops on the platter M1 and then, two platters rotate at a constant angular velocity. W2 M2=6 kg (The moment of inertia of a platter about its center of mass is Iem = /2 mR?). M1 = 8 kg a) Calculate the angular momentum of the platters immediately before the W1 collision. axis of rotation b) Find magnitude and direction of the common angular velocity of the two- platter system immediately after the collision. CHAPTER 11-Angular Momentum; General Rotation PHYS101 c) Is kinetic energy conserved during the collision? (Show a Mathematical proof of your answer) Answers: a) LiF1.8 kgm²/s, L2= -2.4 kgm²/s ; b) -1.25 rad/s rotating clockwise ; c) not conserved
Angular Momentum
The momentum of an object is given by multiplying its mass and velocity. Momentum is a property of any object that moves with mass. The only difference between angular momentum and linear momentum is that angular momentum deals with moving or spinning objects. A moving particle's linear momentum can be thought of as a measure of its linear motion. The force is proportional to the rate of change of linear momentum. Angular momentum is always directly proportional to mass. In rotational motion, the concept of angular momentum is often used. Since it is a conserved quantity—the total angular momentum of a closed system remains constant—it is a significant quantity in physics. To understand the concept of angular momentum first we need to understand a rigid body and its movement, a position vector that is used to specify the position of particles in space. A rigid body possesses motion it may be linear or rotational. Rotational motion plays important role in angular momentum.
Moment of a Force
The idea of moments is an important concept in physics. It arises from the fact that distance often plays an important part in the interaction of, or in determining the impact of forces on bodies. Moments are often described by their order [first, second, or higher order] based on the power to which the distance has to be raised to understand the phenomenon. Of particular note are the second-order moment of mass (Moment of Inertia) and moments of force.
![In the figure, two platters are free to rotate without friction around
8.
the axis of rotation through their centers. Main platter with radius R1 = 30 cm is
rotating with a constant angular velocity of wi = 5 rad/s in counterclockwise
direction. The second platter with radius R2 = 20 cm is rotating with a constant
angular velocity of wz = 20 rad/s in the opposite direction above the platter M,.-
After a time, the platter M2 drops on the platter M1 and then, two platters rotate at
a constant angular velocity.
W2
]M2=6 kg
(The moment of inertia of a platter about its center of mass is Iem = /2mR²).
M1 = 8 kg
a) Calculate the angular momentum of the platters immediately before the
W1
collision.
axis of rotation
b) Find magnitude and direction of the common angular velocity of the two-
platter system immediately after the collision.
CHAPTER 11-Angular Momentum; General Rotation
PHYS101
c) Is kinetic energy conserved during the collision? (Show a Mathematical proof of your answer)
Answers: a) LiFl.8 kgm²/s, L2= -2.4 kgm²/s ; b) -1.25 rad/s rotating clockwise ; c) not conserved](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F89046b93-0e50-4e1e-aa66-1156d5f3f905%2F362f5dee-314f-4d59-920b-1891ceac26f0%2Fq02i4qp_processed.png&w=3840&q=75)
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