When finding Angular Acceleration

[queenspublic]

When finding Angular Acceleration, how is it that -7.129 x 10^-4 rev/s² equal to -4.47800 x 10^-3 rad/sec²? In other words, how does the unit conversion work?

 

[Dr.D]

There are 2*pi rad per rev because a revolution is once around a circle.

 

[nlightner]

Angular acceleration is a measure of the rate at which an object's angular velocity changes over time. It is typically measured in either revolutions per second squared (rev/s2) or radians per second squared (rad/s2). The unit conversion between these two units involves converting from revolutions to radians.

To understand this conversion, we first need to understand the relationship between revolutions and radians. One revolution is equal to 2π radians, which means that one radian is equal to 1/2π of a revolution. This can be written as 1 rad = 1/(2π) rev.

Now, to convert from rev/s2 to rad/s2, we can use the following equation:

Angular Acceleration (rad/s2) = Angular Acceleration (rev/s2) x (1 rad/2π rev)

Substituting the given values, we get:

Angular Acceleration (rad/s2) = -7.129 x 10-4 rev/s2 x (1 rad/2π rev)

= -7.129 x 10-4 x (1/2π) rad/s2

= -4.47800 x 10-3 rad/s2

Therefore, -7.129 x 10-4 rev/s2 is equal to -4.47800 x 10-3 rad/s2. This shows that the unit conversion involves multiplying the value in revolutions per second squared by 1/2π, which is the conversion factor between revolutions and radians.