Finding m/s with revolutions and radius

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Homework Help Overview

The discussion revolves around calculating linear velocity in meters per second (m/s) from the context of circular motion, specifically using the radius of a circle and the time for one complete revolution.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants explore the relationship between revolutions, radians, and linear velocity. Questions arise about converting angular measurements to linear speed and the appropriate formulas to use.

Discussion Status

Some participants have offered calculations and methods, such as using the circumference of the circle and the time for one revolution to find velocity. There is acknowledgment of different approaches, with some suggesting that using angular velocity may simplify the problem.

Contextual Notes

Participants are working with a radius given in kilometers and time in seconds, which may lead to unit conversion considerations. There is also a mention of the need for clarity on angular velocity and its relationship to linear velocity.

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I am confused on how to find m/s in the following problem:

r = 2.6km
one revolution of circle = 360s

I need it for ac = v^2/r

Thanks!,
-Mike
 
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How many radians is 1 revolution?

How do you convert rad/sec to m/s?
 
Well one rev is always 2pi, so 2pi/360s ... I am unsure of how to convert that. I found one solution that tells me to use C = 2(pi)r and v = d/t, so d = 2(pi)(2600m)... so v = 2(pi)(2600m)/360s ... v = 45.4 m/s? Is this the best way to do the problem or am I making it too complicated?
 
That looks right to me.

Angular velocity w = 2 pi / 360, and v is rw

that w is meant to be an omega
 
ah, I see. v = rw does seem a lot more simple than what I did though
 

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