Question

A fan has 2000 J of kinetic energy. If the angular velocity of the fan is doubled,

Answer 1

The new Kinetic energy is 8000 J

Step-by-step explanation:

Step 1 :

Given,

The Kinetic energy of the fan = 2000J

We need to find  new kinetic energy when the angular velocity is doubled.

Step 2 :

We have

KE = $\frac{1}{2 }$ × m × v² = 2000

where m represents the mass and  v represents the singular velocity

v = r ω where

r is radius of  fan and ω is the angular velocity.

Given that the angular velocity is doubled  singular velocity is also doubled. since the radius of the fan is the same in both cases we have

the new velocity = 2rω = 2v

So the KE = $\frac{1}{2}$ m(new velocity)² = $\frac{1}{2}$ m(2v)² = 4 ($\frac{1}{2}$ mv²) = 4 (2000) = 8000 J

Step 3 :

Answer :

The new Kinetic energy is 8000 J