Definition

# radian per second squared

Part of the IT standards and organizations glossary:

The radian per second squared (symbolized rad/s 2 or rad · s -2 ) is the unit of angular (rotational) acceleration magnitude in the International System of Units ( SI ). This is the rate of change of angular speed or velocity. The angular acceleration vector also has a direction component that can be defined in either of two senses: counterclockwise or clockwise.

#### Next Steps

The average angular acceleration magnitude can be obtained by evaluating an object's instantaneous angular speed (in radians per second) at two different points t 1 and t 2 in time, and then dividing the distance by the span of time t 2 - t 1 (in seconds). Suppose the instantaneous angular speed at time t 1 is equal to u 1 , and the instantaneous angular speed at time t 2 is equal to u 2 . Then the average angular acceleration magnitude b avg (in radians per second squared) during the time interval [ t 1 , t 2 ] is given by:

b avg = ( u 2 - u 1 ) / ( t 2 - t 1 )

Instantaneous angular acceleration magnitude is more difficult to intuit, because it involves an expression of rotational motion over an "infinitely short" interval of time. Let p represent a specific point in time. Suppose an object is in rotational motion at about that time. The average angular acceleration magnitude can be determined over increasingly short time intervals centered at p , for example:

[ p -4, p +4]
[ p -3, p +3]
[ p -2, p +2]
[ p -1, p +1]
[ p -0.5, p +0.5]
[ p -0.25, p +0.25]
.
.
.
[ p - x , p + x ]
.
.
.

where the added and subtracted numbers represent seconds. The instantaneous angular acceleration magnitude, b inst , is the limit of the average angular acceleration magnitude as x approaches zero. This is a theoretical value, because it can be obtained only by inference from instantanous speed values determined at the starting and ending points of progressively shorter time spans.

In the complete sense, angular acceleration is a vector quantity having direction as well as magnitude, and representing the rate of change of angular velocity. Suppose, for example, that a wheel's rate of rotation is increasing at 0.5 rad/s 2 in the counterclockwise sense; this might be the case for a car or truck moving from right to left (relative to the viewer) with increasing speed. This would produce an angular acceleration vector with a magnitude of 0.5 rad/s 2 , pointing toward the viewer in line with the wheel's axle. But if the rate of rotation were decreasing at 0.5 rad/s 2 in the counterclockwise sense (the same car or truck slowing down while moving from right to left), the angular acceleration vector would have a magnitude of 0.5 rad/s 2 in the opposite direction, that is, away from the viewer in line with the wheel's axle.

This was last updated in September 2005
Posted by: Margaret Rouse

#### Definitions

- The radian per second (symbolized rad/s or rad/sec) is the Standard International (SI) unit of angular (rotational) speed. (WhatIs.com)

• ##### angular acceleration (rotational acceleration)

- Angular acceleration, also called rotational acceleration, is a quantitative expression of the change in angular velocity that a spinning object undergoes per unit time. (WhatIs.com)

• ##### degree per second squared

- The degree per second squared is an alternative unit of angular (rotational) acceleration magnitude, which is the rate of change of angular speed or velocity. (WhatIs.com)

#### Glossaries

• ##### IT standards and organizations

- Terms related to information technology (IT) standards, including definitions about IT organizations and words and phrases about policies and compliance.

• ##### Computing fundamentals

- Terms related to computer fundamentals, including computer hardware definitions and words and phrases about software, operating systems, peripherals and troubleshooting.

• ##### Internet applications

- This WhatIs.com glossary contains terms related to Internet applications, including definitions about Software as a Service (SaaS) delivery models and words and phrases about web sites, e-commerce ...

#### Dig Deeper

• ##### Hitachi launches 1 TB SATA disk drive

Hitachi has taken the wraps off three new products: a 1 TB enterprise SATA disk drive, a 2.5-inch SAS drive and a 300 GB multi-interface drive. (SearchStorage.com)

• ##### Hitachi launches 1 TB SATA disk drive

Hitachi has taken the wraps off three new products: a 1 TB enterprise SATA disk drive, a 2.5-inch SAS drive and a 300 GB multi-interface drive. (ComputerWeekly.com)

#### Ask An IT Question

Get answers from your peers on your most technical challenges