Two equal point masses (each 1 unit) move with equal constant angular speed in opposite directions on a frictionless circular wire of unit radius. They start together at A (θ = π/2) and meet again at B (θ = -π/2). Which graph shows the magnitude P of their total linear momentum as θ changes? Image (four plots)
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Question

Two equal point masses (each 1 unit) move with equal constant angular speed in opposite directions on a frictionless circular wire of unit radius. They start together at A (θ = π/2) and meet again at B (θ = -π/2). Which graph shows the magnitude P of their total linear momentum as θ changes? Image (four plots)

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G1 Physics · Accepted Answer

Step 1: Both particles move with speed v = ωR = ω (since R = 1) and have momentum magnitude mv. Step 2: At A, their tangential velocities are opposite; total momentum is zero. Step 3: At the side points halfway around, the tangential velocity vectors are parallel downward; momentum magnitude is 2mv. Step 4: At B, the velocities are again opposite, giving zero total momentum. More generally, P = 2mv|cos θ| for θ from π/2 to −π/2. Step 5: Therefore P has a single rounded maximum at θ = 0 and vani…