Two particles of masses m1 and m2 are moving in a circular path of radius r with angular velocities ω1 and ω2 respectively. What is the total angular momentum of the system?
Practice Questions
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Q1
Two particles of masses m1 and m2 are moving in a circular path of radius r with angular velocities ω1 and ω2 respectively. What is the total angular momentum of the system?
(m1 + m2)r(ω1 + ω2)
m1rω1 + m2rω2
m1r^2ω1 + m2r^2ω2
m1ω1 + m2ω2
Total angular momentum L = m1rω1 + m2rω2.
Questions & Step-by-step Solutions
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Q
Q: Two particles of masses m1 and m2 are moving in a circular path of radius r with angular velocities ω1 and ω2 respectively. What is the total angular momentum of the system?
Solution: Total angular momentum L = m1rω1 + m2rω2.
Steps: 7
Step 1: Understand that angular momentum is a measure of how much motion an object has while rotating.
Step 2: Recall that the angular momentum (L) of a single particle moving in a circular path is given by the formula L = m * r * ω, where m is the mass, r is the radius, and ω is the angular velocity.
Step 3: For the first particle with mass m1, radius r, and angular velocity ω1, the angular momentum is L1 = m1 * r * ω1.
Step 4: For the second particle with mass m2, radius r, and angular velocity ω2, the angular momentum is L2 = m2 * r * ω2.
Step 5: To find the total angular momentum of the system, add the angular momentum of both particles: Total angular momentum L = L1 + L2.
Step 6: Substitute the expressions for L1 and L2: L = (m1 * r * ω1) + (m2 * r * ω2).
Step 7: Simplify the expression to get the final formula: Total angular momentum L = m1 * r * ω1 + m2 * r * ω2.
