Atwoods machine and angular momentum

In summary, the conversation discusses the calculation of angular momentum and angular acceleration in a system involving an Atwood's machine with a pulley, two blocks with masses m1 and m2, and a massless string. The formula for angular momentum is discussed, which includes the terms Iw, m1vR, and m2vR. The confusion arises when determining the point to take the angular momentum with respect to, which is clarified to be the center of the pulley. The importance of considering the perpendicular component of the distance and velocity is also highlighted.
  • #1
demonelite123
219
0
so given atwood's machine, a pulley with mass M and radius R, a massless string connected to two blocks with masses m1 and m2 with m1 > m2 and the string does not slip. calculate the angular momentum of the system and use it to find the angular acceleration of the pulley and the linear acceleration of the blocks.

i noticed the book calculate the angular momentum of the system as Iw + m1vR + m2vR. i undestand the pulley having angular momentum Iw but i don't understand why the angular momentum of the blocks being m1vR and m2vR. for a system of particles i know that its just the momentum mv of the particle times the distance of the particle from the point we choose to find the angular momentum with respect to.

im confused because how can the angular momentum of the blocks be m1vR and m2vR when the blocks are connected to strings and they are farther away from the center of the pulley than R? i think I'm confused on which point to take the angular momentum respect to. when i pick the point to be the center of the pulley, it doesn't seem to work out?
 
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  • #2
The point is the center of the pulley. That is for sure.

Angular momentum = r cross mv which means rmvsin(theta). Here r is the distance between the center and m1 and theta is angle between r and v. When you will find (by diagram) rsin(theta) you will get R. So the angular momentum = m1vR.
- ashishsinghal
 
  • #3
You're finding the angular momentum about the axis of the pulley. What's important isn't the displacement vector (distance) that m1 is from the axis of the pulley, but the component of the displacement vector that's perpendicular to the momentum vector, m1v1.
 
  • #4
yeah, you can say so
 
  • #5
you can also say that velocity is not important, velocity perpendicular to displacement vector is important. Mainly, mvrsin(theta) is important, you can approach it in any way.
-ashishsinghal
 
  • #6
ah i see. i forgot about the perpendicular component of the distance. thanks guys!
 

Related to Atwoods machine and angular momentum

1. What is an Atwood's machine?

An Atwood's machine is a simple mechanical device that consists of a pulley, a string, and two masses hanging on opposite sides of the pulley. It is used to demonstrate the principles of classical mechanics, such as Newton's laws of motion and conservation of energy.

2. How does an Atwood's machine work?

An Atwood's machine works by balancing the forces acting on the two masses that are connected by a string passing over a pulley. The difference in the masses causes an imbalance in the forces, resulting in the acceleration of the system. As the masses move, the potential energy of the system is converted into kinetic energy.

3. What is the role of angular momentum in an Atwood's machine?

Angular momentum is a conserved quantity in an Atwood's machine, meaning that it remains constant throughout the system's motion. As the masses move, the angular momentum of the system is conserved due to the conservation of energy and rotational symmetry of the system.

4. How does the length of the string affect an Atwood's machine?

The length of the string in an Atwood's machine affects the acceleration of the system. The longer the string, the greater the distance the masses have to travel, resulting in a longer acceleration time. Therefore, a longer string will result in a slower acceleration, while a shorter string will result in a faster acceleration.

5. What is the significance of an Atwood's machine in science?

An Atwood's machine is significant in science as it helps in understanding the principles of classical mechanics, such as the laws of motion and conservation of energy. It is also used in many real-life applications, such as elevators, cranes, and even amusement park rides.

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