A wheel of mass 23.0 kg and radius 4.0 m is rotating at 3.4 rad/s. Find the rotational kinetic energy of the wheel. (1 wheel = MR^2)

2127.04 J

Explanation:

Rotational kinetic energy can be calculated using the formula;

E(rotational) = 1/2 × I × ω²

Where;

I = moment of inertia

ω = angular velocity

However, the moment of inertia (I) can be calculated using the expression:

I = mr²

Where;

m = mass

r = radius/distance from axis of rotation

According to the provided information, r = 4m, ω = 3.4 rad/s, m = 23kg

I = mr²

I = 23 × 4²

I = 23 × 16

I = 368kg/m²

Hence, if I = 368kg/m², rotational kinetic energy will be:

K = 1/2 × I × ω²

K = 1/2 × 368 × 3.4²

K = 184 × 11.56

K = 2127.04 J