Two particles of masses m1 and m2 are moving in a circular path with radii r1 and r2 respectively. If they have the same angular velocity, what is the ratio of their angular momenta?
Practice Questions
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Q1
Two particles of masses m1 and m2 are moving in a circular path with radii r1 and r2 respectively. If they have the same angular velocity, what is the ratio of their angular momenta?
m1r1/m2r2
m1/m2
r1/r2
m1r2/m2r1
Angular momentum L = mvr, thus L1/L2 = (m1r1)/(m2r2) when ω is constant.
Questions & Step-by-step Solutions
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Q
Q: Two particles of masses m1 and m2 are moving in a circular path with radii r1 and r2 respectively. If they have the same angular velocity, what is the ratio of their angular momenta?
Solution: Angular momentum L = mvr, thus L1/L2 = (m1r1)/(m2r2) when ω is constant.
Steps: 7
Step 1: Understand that angular momentum (L) is calculated using the formula L = mvr, where m is mass, v is linear velocity, and r is the radius of the circular path.
Step 2: Recognize that if two particles are moving in a circular path with the same angular velocity (ω), their linear velocities (v) can be expressed as v = ωr.
Step 3: Substitute the expression for linear velocity into the angular momentum formula: L = m(ωr).
Step 4: For the first particle, the angular momentum L1 = m1(ωr1).
Step 5: For the second particle, the angular momentum L2 = m2(ωr2).
Step 6: To find the ratio of their angular momenta, calculate L1/L2 = (m1(ωr1))/(m2(ωr2)).
Step 7: Since ω is the same for both particles, it cancels out in the ratio, leading to L1/L2 = (m1r1)/(m2r2).
