A child is sitting on the outer edge of a merry-go-round that is 10 m in diameter. If the merry-go-round makes 5 rev/min, what is the velocity of the child in m/s?

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BlackTom AI · Accepted Answer

We start by identifying the given values: a merry-go-round with a diameter of 10 m, so the radius is 5 m. The rotation rate is 5 revolutions per minute.

Option 1: 7.8 m/s. To reach this speed, the tangential velocity would have to be 7.8 m/s, which would require a larger ω or r. Using v = rω with r = 5 m, this would imply ω = v/r ≈ 7.8/5 = 1.56 rad/s, which corresponds to about 0.248 rev/s or 14.9 rev/min—far from the given 5 rev/min. Thus this value is not consistent with the stated rotation.

Option 2: 2.6 m/s. The circumference of the path is C = 2πr = 2π(5 m) = 10π m. At 5 revolutions per minute, the distance traveled per minute is 5 × 10π = 50π m/min. Converting to meters per second: 50π m/min ÷ 60 s/min = (5π)/6 ≈ 2.62 m/s, which rounds to 2.6 m/s. This matches the standard v = rω calculation with r = 5 m and ω = 5 revolutions per minute expressed in radians per second.

Option 3: 4.6 m/s. This value is higher than the correct 2.6 m/s, suggesting either a misapplication of units or a miscalculation of either the radius or rotational speed. The radius is fixed at 5 m, and the given rate is 5 rev/min, so achieving 4.6 m/s would require a different ω than provided.

Option 4: 5.5 m/s. Similar to option 3, this is not compatible with the given data. With r = 5 m, achieving 5.5 m/s would require ω ≈ v/r = 5.5/5 = 1.1 rad/s, which is about 0.175 rev/s or 10.5 rev/min—again inconsistent with the stated 5 rev/min.

In summary, the only option that aligns with v = rω using r = 5 m and 5 revolutions per minute is approximately 2.62 m/s, corresponding to option 2. The other options fail to satisfy the relation between linear speed, radius, and angular speed given in the problem.

SPHY001 Practice Quiz - Unit 06 | LA046

A child is sitting on the outer edge of a merry-go-round that is 10 m in diameter. If the merry-go-round makes 5 rev/min, what is the velocity of the child in m/s?

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