# Difference between linear & rotational motion

Written by james holloway
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In physics, linear motion refers to movement along a straight line, while rotational motion refers to movement around a centre point. Linear and rotational motion are similar in many ways, and the two are often taught together or in sequence. Nonetheless, there are some important differences between the two forms of motion.

## Linear motion

Linear motion describes the change in position of an object moving along a straight line. In the real world, objects seldom move in this fashion -- they move as vectors in three-dimensional space -- but this simple concept of motion makes an ideal introduction to this aspect of physics. In linear motion, the displacement of an object is the distance between its starting and ending points, while its velocity equals its displacement over a certain period of time.

## Rotational motion

While linear motion describes the motion of an object moving along a straight path, rotational motion describes the motion of an object rotating around a fixed axis. Unlike linear motion, rotational motion is described not in terms of the distance between the start and end points of the object's movement, but in the proportion of a complete rotation the object has made. The unit of measurement for rotational motion is radians -- a single radian is 180 degrees divided by pi, or approximately 57.3 degrees.

## Similarities

Rotational and linear motion are similar in many ways. For instance the formula for angular displacement is the difference in radians between its starting and ending positions, while angular velocity is the angular displacement divided by time. These measurements and their formulas are exactly analogous to those used in calculating linear displacement and linear velocity, although the units of measurement and symbols used are different. However, the similarities end there.

## Differences

The main difference between linear and rotational motion is the measurement in radians rather than in linear distance. This has some implications for measuring the velocity and displacement of rotating bodies. Consider the example of two children on a carousel. One is closer to the centre of the carousel than the other. As the carousel rotates, the two children have the same rotational velocity and displacement; they are turning equally rapidly, taking the same amount of time to make a complete revolution. In terms of linear distance, however, the child closer to the edge of the carousel has travelled much further and is going much faster.

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