Angular Velocity Conversions Verify the conversion factor between rpm and rad/s that is listed in Table 8.1. Approach To convert from the dimensions of revolutions per minute to radians per second, we will need conversions for both time and an angle. There are 60 s in 1 min, and 2π rad in one

Question

Angular Velocity Conversions

Verify the conversion factor between rpm and rad/s that is listed in Table 8.1.

Table 8.1
Conversion Factors between Various Units for Angular Velocity

rpm	rps	deg/s	rad/s
1	[latex]1.667×10^{-2}[/latex]	6	0.1047
60	1	360	6.283
0.1667	[latex]2.777×10^{-3}[/latex]	1	1.745×10^{-2}[/latex]
9.549	0.1592	57.30	1

Approach

To convert from the dimensions of revolutions per minute to radians per second, we will need conversions for both time and an angle. There are 60 s in 1 min, and 2π rad in one revolution.

Accepted Answer

We convert dimensions as follows:

[latex]1\frac{rev}{min} =\left(1\frac{rev}{min} \right)\left(\frac{1}{60}\frac{min}{s} \right)\left(2\pi \frac{rad}{rev} \right) [/latex]

[latex]= 0.1047 \left(\frac{\cancel {rev}}{\cancel {min}} \right)\left(\frac{\cancel {min}}{s} \right)\left(\frac{rad}{\cancel {rev}}\right) [/latex]

[latex]=0.1047 \frac{rad}{s} [/latex]

Discussion
We can obtain the inverse conversion factor between rad/s and rpm as the reciprocal of this quantity, so that [latex] 1 rad/s = (0.1047)^{-1} rpm = 9.549 rpm. [/latex]

[latex] 1 rpm = 0.1047 \frac{rad}{s} [/latex]

Question 8.1: Angular Velocity Conversions Verify the conversion factor be...

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