2 hard angular momentum problems

In summary: In the Atwood's Machine problem, there are two masses, M and 2M, connected by a massless string over a pulley. The pulley is a uniform disk with mass M and radius R. The string does not slip with respect to the pulley. Using conservation of energy, the acceleration can be found to be a=2g/7. In the coin problem, the coin is projected forward with speed V and angular speed w, and has a coefficient of kinetic friction u with the table. The goal is to find V and w so that the coin comes to a rest a distance d from where it started. To approach this problem, use the general equations L=rxp and t=dL/dt, along
  • #1
Krdall
1
0

Homework Statement


the easier one
Atwood's Machine. The masses are M and 2M, and the pulley is a uniform disk of mass M and radius R. the string is massless and does not slip with respect to the pulley. Find the acceleration of the masses. Use force and Torque.
answer should be something like a=2g/7 (using conservation of energy) but i only care about how to get there using force and torque

The harder one
A coin stands vertically on a table. It is projected forward (in the plane if itself) with speed V and angular speed w. The coefficient of kinetic friction between the coin and the table is u. What should V and w be so that the coin comes to a rest(both translationally and rotationally) a distance d from where it started.
the coin in this problem has a backward spin. it is not rolling forward.

I know the general equations here I am really just looking for a prob in the right direction. I really do not know how to approach these questions.

Homework Equations


L=rxp
t=dL/dt
t=rxF
dL/dt=d/dt(rxp)
 
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  • #2
As always with force and torque problems, start by identifying the forces acting on the body and drawing a free-body diagram.
 

1. What is angular momentum?

Angular momentum is a physical quantity that represents the rotational motion of an object around a fixed point or axis. It is defined as the product of an object's moment of inertia and its angular velocity.

2. How is angular momentum calculated?

Angular momentum is calculated using the formula L = Iω, where L is angular momentum, I is moment of inertia, and ω is angular velocity. The units for angular momentum are kilogram-meter squared per second (kg·m2/s).

3. What are "hard" angular momentum problems?

"Hard" angular momentum problems are those that involve complex systems with multiple objects and/or changing rotational speeds. These types of problems require a more advanced understanding of angular momentum and may involve using equations from classical mechanics or quantum mechanics.

4. How can I solve "hard" angular momentum problems?

To solve "hard" angular momentum problems, it is important to first identify and understand all the given information and variables. Then, one can use the relevant equations and principles of angular momentum, such as conservation of angular momentum, to solve for the unknown quantities.

5. What are some real-life applications of angular momentum?

Angular momentum has many real-life applications, such as in the design of satellites and spacecrafts, the motion of planets and other celestial bodies, and the behavior of spinning objects like gyroscopes. It is also important in understanding the motion of atoms and particles in quantum mechanics.

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