Rick S.

asked • 12/23/12# Is it legal to add a unitless number to a number with units?

If not what is the procedure for solving for r in the equation:(35m/s)sqd/r = -0.0021-0.0026m/(s)sqd. The answer should be in m for meters. S=seconds. Thank you! Rick

## 2 Answers By Expert Tutors

Daniel O. answered • 12/26/12

Math and Physics Tutor, with a math and physics degree

Rick, it'd probably be better to post the whole question - we have physics tutors here such as myself and Sung.

Sung taee L. answered • 12/26/12

Teach Concepts, Thinking methods, Step by Step (Physics & Math)

Dear Rick

If the used units are considered, your given equation looks as this.

Centripetal acceleration + angular velocity * linear velocity = 1/density * density

And this can be simplified by

Acceleration + acceleration = unitless

This is totally wrong in physics.

All the units[ actually dimensions ] used in the equation should be the same otherwise the equation itself is meaningless.

For example:

2 apple + 3 pear = 5 grape

This equation is meaningless.

2 apple + 3 apple = 5 apple

This has meaning. Like this, units work like fruits in this example.

I think the unit for right side is wrong in certain way, because for left side two terms using the same dimension such as acceleration. I guess you miss gravitational acceleration for right side.

Hope this help you.

Rick S.

The answer is finally solved! To convert mb to MKS, one may write:

1 mb = 100 N/m^{2} ; noting that N = kg m/sec. The dimensions work out to meters when solving for r. Which is solved as 52,350 meters.

Thank you all for your help over the Christmas Holiday!

Have a safe 2013! Rick

12/27/12

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Bill F.

I assume the (35m/s)sqd = (35m/s)

^{2}, and that is divided by r. But I don't understand the right side of the equation: Is the -0.0021 also m/s, and is the -0.0026m/(s)sqd actually (-0.0026m/s)^{2 }??12/23/12