Question

A fan is starting from rest with a constant angular acceleration of 3rad/s². What will be its angular speed (in rad/s ) after it makes 50 revolutions?

Answer 1

The angular speed of the fan after it makes 50 revolutions is approximately 77.46 rad/s.

Step-by-step explanation:

To find the angular speed of the fan after 50 revolutions, we can use the equation:

ω^2 = ω^20 + 2αθ

Where ω^2 is the final angular speed, ω^20 is the initial angular speed (which is 0 since the fan starts from rest), α is the constant angular acceleration (3 rad/s²), and θ is the angle through which the fan rotates (in this case, 50 revolutions).

Plugging in the values, we have:

ω^2 = 0 + 2(3 rad/s²)(50 revolutions)(2π rad/revolution)

Simplifying the equation gives:

ω^2 = 600π rad²/s²

Taking the square root of both sides gives:

ω = √(600π) rad/s

Using a calculator to find the approximate value, we get:

ω ≈ 77.46 rad/s