Concept question: Angular momentum

• jegues
In summary, a pulley with radius R and rotational inertia I is attached to two blocks of mass m1 and m2 by a massless string. At a certain time, m1 is moving downward with speed v. When considering the system of the blocks and the pulley, the magnitude of the total angular momentum can be calculated using the equation L = l1 + l2 + l3... where l represents the angular momentum, r represents the radius, and p represents the linear momentum. The direction of the radius matters when calculating the angular momentum, as shown by the two r vectors pointing in opposite directions for the two masses.
jegues

Homework Statement

A pulley with radius R and rotational inertia I is free to rotate on a horizontal fixed axis through its center. A massless string passes over the pulley. A block of mass m1 is attached to one end and a block of mass m2 is attached to the other. At one time the block with mass m1 is moving downward with speed v. If the string does not slip on the pulley, the magnitude of the total angular momentum, about the pulley centre, of the blocks and the pulley, considered as a system is given by:

Homework Equations

L = l1 + l2 + l3...

l = rxp
l = Iw

The Attempt at a Solution

In my diagram.

I may have answered my question by rewriting the question out, but I'd like to double check.

Is the v on m2 not negative because the question says the magnitude?

Thanks again,

Attachments

• speedquestion.JPG
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L = mr x v. If for one mass you take r positive and v also positive, then for the other mass both r and v are negative which means that the angular momentum of the other mass is also positive.

How can the radius for the other mass be negative?

Note that I put r in bold. That means that it is a vector. If you draw the two r's, you will see that they point in opposite directions. Angular momentum is also a vector, so direction matters when you add two angular momenta together.

1. What is angular momentum?

Angular momentum is a physical quantity that describes the rotational motion of an object. It is a vector quantity, meaning it has both magnitude and direction, and is defined as the product of an object's moment of inertia and its angular velocity.

2. How is angular momentum different from linear momentum?

Unlike linear momentum, which describes the motion of an object in a straight line, angular momentum describes the rotational motion of an object around a fixed point. Additionally, linear momentum is conserved in all inertial reference frames, while angular momentum is conserved only in systems with no external torque.

3. How is angular momentum related to torque?

Torque is the rotational equivalent of force, and is defined as the product of force and the distance from the pivot point. In a system with no external torque, the angular momentum is conserved, meaning that the total angular momentum before an event is equal to the total angular momentum after the event.

4. What are some examples of angular momentum in real life?

Angular momentum can be observed in many everyday situations, such as the rotation of a spinning top, the movement of a gyroscope, the orbit of planets around the sun, and the spinning of a figure skater during a performance.

5. How is angular momentum used in the field of science?

Angular momentum is a fundamental concept in many areas of science, including physics, engineering, and astronomy. It is used to understand the behavior of rotating systems, such as the motion of planets and galaxies, and to design machines and structures that rely on rotational motion, such as turbines and propellers.

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