Conversion of translational momentum to angular momentum

In summary, two masses, m1 and m2, collide and become a single system when m1 attaches to a bar attached to m2. To find the resulting translational and angular velocities of the system, conservation of linear and angular momentum equations must be written, using a chosen point to calculate initial and final angular momenta.
  • #1
appa609
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Suppose there was a mass, m1, traveling rightwards at v0. There is a second mass, m2, above the line of motion of m1, and which has a rigid, massless bar of length L attached to its center of mass. This bar extends downwards so that the terminal intersects with the path of m1. When m1 reaches this intersection, it attaches to the bar at its own center of mass, and m1 and m2 move as a single system. How can one find the resulting translational and angular velocities of the final system?
 
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  • #2
Your title is misleading. Linear momentum and angular momentum are separately conserved. Let final velocities of m1 and m2 be v1 and v2. Write down equations embodying conservation of linear mometum and conservation of angular momentum. You will have to choose a point about which to calculate initial and final angular momenta.
 
  • #3
Thank you.
 

1. What is the concept of conversion of translational momentum to angular momentum?

The conversion of translational momentum to angular momentum refers to the transfer of momentum from an object's linear motion to its rotational motion. This occurs when a force is applied at a distance from the object's center of mass, causing it to rotate.

2. What is the relationship between translational and angular momentum?

Translational momentum and angular momentum are both measures of an object's motion. Translational momentum is a measure of an object's linear motion, while angular momentum is a measure of its rotational motion. The two are related through the moment of inertia, which is a measure of an object's resistance to change in rotational motion.

3. How is translational momentum converted to angular momentum?

Translational momentum can be converted to angular momentum through the application of a force at a distance from an object's center of mass. This force creates a torque, which causes the object to rotate and results in the conversion of translational momentum to angular momentum.

4. What is the conservation of momentum principle in relation to conversion of translational to angular momentum?

The conservation of momentum principle states that the total momentum of a system remains constant unless an external force is applied. In the case of conversion of translational to angular momentum, the total momentum of the system remains constant as long as there is no external torque acting on the system.

5. What are some real-life examples of conversion of translational to angular momentum?

A common example of conversion of translational to angular momentum is seen in a spinning top. When a force is applied to the top, it begins to rotate around its axis, converting its translational momentum into angular momentum. Another example is seen in the motion of a planet around the sun, where gravitational force causes the planet to rotate and convert its translational momentum into angular momentum.

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