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Lekcja 1: Wprowadzenie do ruchu obrotowego

Introduction to rotational motion review

Overview of key terms, equations, and skills for rotational motion, including the difference between angular and tangential acceleration.

Term (symbol)	Meaning
Axis of rotation	The imaginary or actual axis around which an object may rotate.
Average angular acceleration ( $α$ ‍)	Measure of how angular velocity changes over time. The rotational analogue of linear acceleration. A vector quantity with counterclockwise defined as the positive direction. SI units of $\frac{radians}{s^{2}}$ ‍.
Tangential acceleration ( $a_{t}$ ‍)	Linear acceleration of a rotating object that is perpendicular to its radial acceleration. SI units of $\frac{m}{s^{2}}$ ‍.

Equation	Symbols	Meaning in words
$v = ω r$ ‍	$v$ ‍ is linear speed, $ω$ ‍ is angular speed, and $r$ ‍ is radius	The linear speed is proportional to the angular speed and the radius.
$α = \frac{Δ ω}{Δ t}$ ‍	$α$ ‍ is average angular acceleration, $Δ ω$ ‍ is change in angular velocity, and $Δ t$ ‍ is change in time	The average angular acceleration is the change in angular velocity divided by time.
$a_{t} = α r$ ‍	$a_{t}$ ‍ is tangential acceleration	The tangential acceleration is proportional to the angular acceleration and the radius.

People sometimes mix up angular and tangential (or linear) acceleration. Angular acceleration is the change in angular velocity divided by time, while tangential acceleration is the change in linear velocity divided by time.
People sometimes forget that angular acceleration does not change with radius, but tangential acceleration does. For example, for a rotating wheel that is speeding up, a point on the outside covers more distance in the same amount of time as a point closer to the center. It has a much larger tangential acceleration than the portion closer to the axis of rotation. However, the angular acceleration of every part of the wheel is the same because the entire object moves as a rigid body through the same angle in the same amount of time.

To check your understanding and work toward mastering these concepts, check out the exercises in this tutorial.

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