Two particles A and B of masses m1 and m2 are moving in opposite directions with velocities v1 and v2 respectively. What is the total angular momentum of the system about the origin if they are at a distance r from the origin?
Practice Questions
1 question
Q1
Two particles A and B of masses m1 and m2 are moving in opposite directions with velocities v1 and v2 respectively. What is the total angular momentum of the system about the origin if they are at a distance r from the origin?
m1v1r + m2v2r
m1v1r - m2v2r
m1v1r + m2(-v2)r
0
Total angular momentum L = m1v1r - m2v2r, but since they are in opposite directions, it simplifies to m1v1r + m2v2r.
Questions & Step-by-step Solutions
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Q
Q: Two particles A and B of masses m1 and m2 are moving in opposite directions with velocities v1 and v2 respectively. What is the total angular momentum of the system about the origin if they are at a distance r from the origin?
Solution: Total angular momentum L = m1v1r - m2v2r, but since they are in opposite directions, it simplifies to m1v1r + m2v2r.
Steps: 8
Step 1: Understand that angular momentum (L) is a measure of the rotational motion of an object around a point, in this case, the origin.
Step 2: Recall the formula for angular momentum of a particle, which is L = m * v * r, where m is mass, v is velocity, and r is the distance from the point of rotation (the origin).
Step 3: Identify the two particles: Particle A with mass m1 moving with velocity v1 and Particle B with mass m2 moving with velocity v2.
Step 4: Note that Particle A is moving in one direction and Particle B is moving in the opposite direction.
Step 5: Write the angular momentum for Particle A: L_A = m1 * v1 * r.
Step 6: Write the angular momentum for Particle B: L_B = m2 * v2 * r. Since it is moving in the opposite direction, we consider its angular momentum as negative: L_B = -m2 * v2 * r.
Step 7: Combine the angular momenta of both particles: Total angular momentum L = L_A + L_B = m1 * v1 * r - m2 * v2 * r.
Step 8: Since the particles are moving in opposite directions, we can simplify the equation to L = m1 * v1 * r + m2 * v2 * r.
