Common Mistakes

The Basics of Rotation

Radians, radians, radians. Use them, know them, love them. There are 2π rad in one rotation.

Moment of Inertia

Remember the moments listed for common shapes are only true if the axis of rotation goes through the center of mass in the direction indicated. For an axis of rotation located at a different point (but in the same direction), we can use the parallel axis theorem to get the correct moment of inertia; for a different direction of rotation the moment of inertia may be completely different.

Torque

Torque is a product of force and distance—but also a function of the angle between force and distance. Don't forget the sin θ in τ = rF sin θ.

Angular Momentum

Angular momentum and translational momentum are completely analogous—but that does not make them identical. They have different units, and describe different motion.

Rotation and Energy

Rotational energy, work, and power are all convertible to their translational equivalents, and are measured in the same units. This is very different than angular velocity, acceleration, and momentum, which are all only analogous to their translational counterparts—and measured in different units.