The angular speeds of each of a body moving at 10 revolutions per second is:

Question

BlackTom AI · Accepted Answer

The problem asks for the angular speed when the body is moving at 10 revolutions per second.

Option 1: 75.4 rad/s. To check this, convert revolutions per second to radians per second: ω = 2πf, so with f = 10 s⁻¹, ω = 2π × 10 = 20π ≈ 62.8 rad/s. The value 75.4 rad/s would correspond to f ≈ 75.4 / (2π) ≈ 12 rev/s, which is not the given speed. This makes this option incorrect.

Option 2: 62.8 rad/s. This matches the conversion ω = 2πf with f = 10 s⁻¹, since ω = 2π × 10 = 20π ≈ 62.8 rad/s. This is consistent with the stated speed and is dimensionally correct.

Option 3: 20.1 rad/s. If ω = 20.1 rad/s, then f = ω / (2π) ≈ 20.1 / 6.283 ≈ 3.2 rev/s. This does not equal the given 10 rev/s, so this option is incorrect.

Option 4: 43.5 rad/s. Here, f = ω / (2π) ≈ 43.5 / 6.283 ≈ 6.9 rev/s. Since this is not 10 rev/s, this option is also incorrect.

Summary: The correct approach is to use the relation ω = 2πf to convert revolutions per second to radians per second. Only the value 62.8 rad/s coincides with f = 10 s⁻¹, while the other numbers correspond to different frequencies and thus are inconsistent with the given speed.

SPHY001 Practice Quiz - Unit 06 | LA046

The angular speeds of each of a body moving at 10 revolutions per second is:

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