Question

When a ceiling fan is switched on, it makes 10 rotations in the first 3 second. How many rotations will it make in the next 3 second? (Assume uniform angular acceleration)

Options

• 10

• 20

• 30

• 40

Answer 1

30

Explanation:

ω = 2πn = `ω_it + 1/2 αt^2`

∴ `2pi xx 10 = 1/2 alpha xx 3^2`

∴ α = `(40pi)/9`

Allow it to rotate N times in the first 6 seconds.

∴ 2πn = `1/2 alpha(6)^2`

∴ N = `1/(2pi) 36/2 (40pi)/9` = 40

∴ The number of rotations required = 40 – 10 = 30