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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 start fraction, start text, r, a, d, i, a, n, s, end text, divided by, start text, s, end text, squared, end fraction.
Tangential acceleration (a, start subscript, t, end subscript)Linear acceleration of a rotating object that is perpendicular to its radial acceleration. SI units of start fraction, start text, m, end text, divided by, start text, s, end text, squared, end fraction.

## Equations

EquationSymbolsMeaning in words
v, equals, omega, rv is linear speed, omega is angular speed, and r is radiusThe linear speed is proportional to the angular speed and the radius.
alpha, equals, start fraction, delta, omega, divided by, delta, t, end fractionalpha is average angular acceleration, delta, omega is change in angular velocity, and delta, t is change in timeThe average angular acceleration is the change in angular velocity divided by time.
a, start subscript, t, end subscript, equals, alpha, ra, start subscript, t, end subscript 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.