Angular Momentum of Colliding Pucks: 80g & 120g Mass, 4cm & 6cm Radius

[vijay123]

dear ppl,
a puck of mass 80g and radius 4cm slides along an air table at a speed of 1.5m/s. it makes a glancing collision with a second puck of radius 6cm and mass 120g. because their rims are coated with glue, the stick together and spin after the collison. find their angular velocity.

the ans is 9 rad/s but i keep getting 19 rad/s. my doubt is that does the puck that slides carry any angular momentum by itself? i think it doesn't have coz its sliding but i am not sure...thanks

 

[Doc Al]

While the sliding puck has zero angular momentum about its center of mass, it certainly has angular momentum about the center of mass of the two puck system. (And it's the angular momentum of the system that remains the same.) Hint: What's the velocity of the center of mass?

 

[kyle8921]

I can confirm that the puck that is sliding does not have any angular momentum by itself. Angular momentum is a property of an object's rotational motion, and the sliding puck only has linear motion. Therefore, the initial angular momentum of the system is only due to the second puck with a mass of 120g and a radius of 6cm.

To calculate the final angular velocity of the combined pucks, we can use the principle of conservation of angular momentum, which states that the total angular momentum of a system remains constant in the absence of external torques. In this case, the initial angular momentum of the system is equal to the final angular momentum after the collision.

Using the formula for angular momentum, L = Iω, where I is the moment of inertia and ω is the angular velocity, we can set up the following equation:

Linitial = Lfinal

(120g)(6cm)^2(1.5m/s) = (120g + 80g)(6cm + 4cm)^2ωfinal

Solving for ωfinal, we get 9 rad/s as the final angular velocity of the combined pucks. It is possible that you may have made a calculation error in your calculations, which resulted in a different value for the final angular velocity. I would recommend double-checking your calculations to ensure accuracy.