How Do You Calculate Angular Momentum in a Two-Particle System?

In summary, the problem involves two particles of mass m1 and m2 connected by a string of length L. The system is on a smooth horizontal plane with the string tight. Mass m1 is projected perpendicular to the string at speed v0. The problem asks to find the center of mass speed and the angular speed of the system, as well as the linear speeds of the individual masses after the attack. It is suggested to ask for the tension in the string and show that m2 follows a cycloid to solve this problem.
  • #1
atuntun
1
0

Homework Statement



Two particle of mass m1 and m2 are connected by an inextensible and massless string of length L. The system is placed on a smooth and horizontal plane with the string being kept tight. Mass m1 is projected along a direction which is normal to the string and the speed is v0.
a). Find the speed of the center of mass of the system and the angular speed of the system about its center of mass.
b).Hence, find the linear speeds of the individual masses just after the attack.


Thank you in advance for the help!
 
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  • #2
Please read our policy on homework help. You need to show some effort before we give help.
 
  • #3
Weird question.

The answer to part b) is effectively given in the question, and is needed
to answer part a).

Why not ask for the tension in the string, and show that m2 follows a cycloid?
 

1. What is angular momentum?

Angular momentum is a measure of the rotational motion of an object around an axis. It is the product of an object's moment of inertia and its angular velocity.

2. How is angular momentum calculated?

Angular momentum is calculated by multiplying an object's moment of inertia (a measure of its resistance to rotational motion) by its angular velocity (the rate at which it rotates around an axis).

3. What are the units of angular momentum?

The units of angular momentum are kilogram meters squared per second (kg·m²/s) in the SI system, or pound feet squared per second (lb·ft²/s) in the imperial system.

4. How does angular momentum relate to conservation of momentum?

Angular momentum is conserved in a closed system, meaning that the total amount of angular momentum remains constant even if the objects within the system are moving or rotating. This is similar to the concept of conservation of linear momentum, where the total amount of momentum remains constant in a closed system.

5. Can angular momentum be negative?

Yes, angular momentum can be negative. This typically occurs when an object is rotating in the opposite direction of a chosen axis, resulting in a negative value for its angular velocity. However, the magnitude of the angular momentum remains the same regardless of its sign.

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