Robin (R) and Sanji (S) are riding a merry-go-round that is spinning steadily. Sanji is twice as far from the axis as is Robin, as shown below. How do their angular velocity ω and angular acceleration α compare? ωR = ωs and αR = αS ωR < ωs and αR > αS ωR < ωs and αR < αS ωR = ωs and αR < αS
Question
Robin (R) and Sanji (S) are riding a merry-go-round that is spinning steadily. Sanji is twice as far from the axis as is Robin, as shown below. How do their angular velocity ω and angular acceleration α compare? ωR = ωs and αR = αS ωR < ωs and αR > αS ωR < ωs and αR < αS ωR = ωs and αR < αS
Solution
The correct answer is ωR = ωS and αR = αS.
Here's why:
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Angular velocity (ω): This is the rate at which an object moves through an angle. In a spinning merry-go-round, all points (including Robin and Sanji) make a full circle in the same amount of time. Therefore, they have the same angular velocity.
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Angular acceleration (α): This is the rate of change of angular velocity. If the merry-go-round is spinning steadily, it means there is no change in angular velocity. Therefore, the angular acceleration is zero for all points (including Robin and Sanji).
So, regardless of their distance from the axis, Robin and Sanji have the same angular velocity and angular acceleration.
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