Rotational Motion Vocabulary

This set of vocabulary flashcards covers the fundamental concepts of rotational motion, including angular displacement, radians, degrees, and arc length formulas based on the lecture notes.

Rotational motion

The motion of an object around a central point or axis, occurring when an object spins around a fixed point so that all its parts move in circular paths.

Circular Motion

Motion where an object moves around an external center, typically studied as a single particle moving along a circle.

Revolution

A measurement of how many times an object completes a full turn, helping to describe how fast an object rotates and how much it has turned.

Degree

A unit of measurement for a fraction of a revolution where one full revolution is equal to $360^\circ$.

Radian

The angle formed when the arc length is equal to the radius of the circle, where one full revolution is equal to $2\pi$ radians.

Angular displacement ($\Delta \theta$)

The change in the angle as an object rotates, represented by the Greek letter theta ($\theta$).

Positive Angular Displacement

The designation for rotation occurring in a counterclockwise direction.

Negative Angular Displacement

The designation for rotation occurring in a clockwise direction.

Arc length

The length along a circular path, defined as the product of the radius and the angle in radians: $s = r\theta$.

Distance formula for rotation ($x = r\theta$)

Used to find the distance traveled along a circular path for a rotation through an angle $\theta$ at a distance $r$ from the center.

Conversion: Degree to Radian

The process of finding radian measure by multiplying the degree by $\frac{\pi}{180}$, e.g., $60^\circ = 60 \times \frac{\pi}{180} = \frac{\pi}{3}$.

Conversion: Radian to Degree

The process of finding degree measure by multiplying the radian value by $\frac{180}{\pi}$, e.g., $\frac{2\pi}{3} \times \frac{180}{\pi} = 120^\circ$.

One Full Rotation (Value)

Equivalent to $2\pi$ radians or approximately $6.28\,rad$.