Question

A large aluminum drum (solid cylinder) with a radius of 0.8 m and a mass of 650 kg is rotating at 10rev/min about an axis through its center. What is its rotational kinetic energy (in Joules)?

A) 208 J
B) 1040 J
C) 436 J
D) 109 J

Answer 1

The rotational kinetic energy of the aluminum drum can be calculated using the formula KE_rot = 0.5 * I * ω². Substituting the given values for the moment of inertia and angular velocity, we find that the rotational kinetic energy is 208 Joules.

Step-by-step explanation:

The rotational kinetic energy of a rotating object can be calculated using the formula KErot = 0.5 * I * ω², where I is the moment of inertia and ω is the angular velocity.

In this case, the moment of inertia of the aluminum drum can be calculated using the formula I = 0.5 * M * R², where M is the mass of the drum and R is its radius.

Substituting the given values, we have:

I = 0.5 * 650 kg * (0.8 m)² = 208 kg·m²

Converting the rotational speed from revolutions per minute to radians per second, we have:

ω = (10 rev/min) * (2π rad/rev) * (1 min/60 s) = 1.05 rad/s

Substituting the values of I and ω into the formula for KErot, we get:

KErot = 0.5 * 208 kg·m² * (1.05 rad/s)² = 208 J