Two circular pucks, each of mass M and radius R, slide toward each other and are about to collide on frictionless ice. The pucks have glue on their edges and when they collide the pucks will stick together.
Before the collision, the rightward-travelling puck has speed 2v and is not rotating; the leftward-travelling puck has speed v and rotates with angular velocity ω, which could be positive or negative.
For the reference point shown in the figure , what is the initial angular momentum of each puck? Answer in terms of M, R, v, and ω
Lupper,i=
unanswered
Llower,i=
unanswered
CHECK YOUR ANSWER SAVE YOUR ANSWER You have used 0 of 3 submissions
Quiz 12, Problem 3 (B)
(1 point possible)
For this part, use whatever reference point you like.
What initial value of the angular velocity ω guarantees that the two-puck system will not be rotating after the collision? Answer in terms of R, M, and v; be sure to indicate the sign of ω .
ω=
unanswered
To find the initial angular momentum of each puck, we need to understand the concept of angular momentum. Angular momentum is the rotational analog of linear momentum and is defined as the product of moment of inertia and angular velocity.
The moment of inertia of a circular puck of mass M and radius R can be given as 1/2 MR^2. Therefore, the initial angular momentum of the upper puck (Lupper,i) can be calculated as:
Lupper,i = Moment of inertia * Angular velocity
Lupper,i = (1/2 MR^2) * 0
Since the upper puck is not rotating initially, its angular velocity is zero and hence, the initial angular momentum of the upper puck (Lupper,i) is also zero.
On the other hand, the lower puck is rotating with an angular velocity ω. The initial angular momentum of the lower puck (Llower,i) can be calculated as:
Llower,i = Moment of inertia * Angular velocity
Llower,i = (1/2 MR^2) * ω
Now, to find the initial value of the angular velocity ω that guarantees that the two-puck system will not be rotating after the collision, we need to use the principle of conservation of angular momentum. According to this principle, the total angular momentum before the collision should be equal to the total angular momentum after the collision.
Since the upper puck is not rotating before the collision, its angular momentum is zero. Hence, we only need to consider the initial angular momentum of the lower puck.
After the collision, the two pucks stick together and move as one object. If the two-puck system is not rotating after the collision, the net angular velocity should be zero. Therefore:
Llower,i = (1/2 MR^2) * ω = 0
Solving this equation, we find that ω = 0. This means that the initial value of the angular velocity ω that guarantees that the two-puck system will not be rotating after the collision is zero.
Therefore, the answer to the second part of the question is ω = 0.