An amusement park ride is a giant barrel with I = 15400 kg•m2. How much work does it take to speed the barrel from rest to 3.14 rad/s?

Answer 1

Let

I = 15400 kgm² be the moment of inertia,

ω = 3.14 s^-1 be the angular velocity,

W (to be calculated) be the work needed to achieve ω,

E (unknown) be the rotational energy of the barrel at ω.

Assuming no resistance to motion,

W = E

The formula for

E = Iω²/2 = 15400 kgm² × 3.14² s^-2 / 2 = 75918.92 J