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## Mechanics (Essentials) - Class 11th

### Course: Mechanics (Essentials) - Class 11th>Unit 12

Lesson 1: How do spinning wheels and moving cars connect? Uncovering the link between angular and linear motion!

# Introduction to rotational motion review

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

## Key terms

Term (symbol)Meaning
Axis of rotationThe imaginary or actual axis around which an object may rotate.
Average angular acceleration ($\alpha$)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 $\frac{\text{radians}}{{\text{s}}^{2}}$.
Tangential acceleration (${a}_{t}$)Linear acceleration of a rotating object that is perpendicular to its radial acceleration. SI units of $\frac{\text{m}}{{\text{s}}^{2}}$.

## Equations

EquationSymbolsMeaning in words
$v=\omega r$$v$ is linear speed, $\omega$ is angular speed, and $r$ is radiusThe linear speed is proportional to the angular speed and the radius.
$\alpha =\frac{\mathrm{\Delta }\omega }{\mathrm{\Delta }t}$$\alpha$ is average angular acceleration, $\mathrm{\Delta }\omega$ is change in angular velocity, and $\mathrm{\Delta }t$ is change in timeThe average angular acceleration is the change in angular velocity divided by time.
${a}_{t}=\alpha r$${a}_{t}$ is tangential accelerationThe tangential acceleration is proportional to the angular acceleration and the radius.

## Common mistakes and misconceptions

1. 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.
2. 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.

For deeper explanations of angular quantities, see our videos angular motion variables and relating angular and regular motion variables
To check your understanding and work toward mastering these concepts, check out the exercises in this tutorial.

## Want to join the conversation?

• Are rotational motion and angular motion are same thing ? Or are they two different things ?
(1 vote)
• I think they're the same thing. The actual name is angular velocity and angular acceleration.
• Why do we need to take the reciprocal of angular acceleration after we use a = R alpha?
• why angular frequency remains constant whereas time period is not constant
(1 vote)
• Think of angular frequency as the number of times a point on the circle completes a revolution in a given amount of time (for SI units, it would be in one second). Though time period for which it is measured may not be constant, the point will still go the same number of revolutions in a single second regardless of whether you are measuring for one second or 2 seconds or even 5 seconds.
(1 vote)
• Is rotational motion dimensionless
(1 vote)
• The dimensional formula of angular displacement is [ L ] [ L ] = 1 OR dimensionless. Hence, it does not have any dimension and it is true that it will not have any units, but for some reason, it has been given a SI unit i.e. radians. Another unit is degree.
(1 vote)
• How do you figure out which type of acceleration the problem id giving to you if it does not have units. Ex) A n object with a diameter of 36m is turning about an axis at a constant rate. How would I know that thats angular acceleration?
(1 vote)
• The author of this article made a mistake, v should be defined as speed of object.
• v (aka speed) is also known as the linear velocity (or tangential velocity), as it is the instantaneous velocity of the object at that point in the rotational motion
• Introduction to rotational motion
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