Finding m/s with revolutions and radius

• Visual1Up
In summary, to find m/s in the given problem, we need to use the formula ac = v^2/r. To convert radians to m/s, we can use the formula w = 2pi/360 and v = rw. Using this, we can simplify the problem and find that v = 45.4 m/s.
Visual1Up
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

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

1. How do I find the linear speed in m/s using revolutions and radius?

To find the linear speed in m/s, you can use the formula v = 2πrN, where v is the linear speed in m/s, π is the mathematical constant pi, r is the radius in meters, and N is the number of revolutions per second.

2. Can I use this formula for any type of circular motion?

Yes, this formula can be used for any type of circular motion as long as the linear speed is constant and the radius remains the same.

3. What is the relationship between revolutions and linear speed?

The relationship between revolutions and linear speed is direct. As the number of revolutions per second increases, the linear speed also increases.

4. How can I convert the units of revolutions and radius to match the units of linear speed?

To convert the units, you can use unit conversion factors. For example, if the radius is given in centimeters, you can convert it to meters by multiplying it by a factor of 0.01. Similarly, if the number of revolutions is given in revolutions per minute, you can convert it to revolutions per second by dividing it by 60.

5. Can I use this formula to find the linear speed if the angular speed is given?

Yes, you can use this formula to find the linear speed if the angular speed is given. The angular speed is equal to 2πN, where N is the number of revolutions per second. So, you can substitute this value for N in the formula v = 2πrN to find the linear speed.

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