MHB Find the diameter of a circle given linear velocity?

AI Thread Summary
To find the diameter of a circular object given its linear velocity, the formula v = ωr is used, where v is linear velocity, ω is angular velocity, and r is the radius. In the example provided, the linear velocity of 19 mph is converted to 1672 ft/min, and the angular velocity for 10 revolutions per minute is calculated as 20π radians/min. The radius can then be determined using the rearranged formula r = v/ω, leading to the diameter being d = 2v/ω. The discussion emphasizes the importance of unit conversion for accurate calculations. Ultimately, the diameter can be derived from these values.
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[SOLVED] Find the diameter of a circle given linear velocity?

Hello all! I need help with a certain type of problem. I do not know how I can find the diameter of a circular object given it's linear velocity. Here is an example problem, and I would love any explanation you could give me! Thanks! :))

Leaving the Ferris Wheel, Daniel sees his friend, Jenna, riding the Super Circle Swings. As he watches, she goes around 10 times in one minute. The sign on the ride claims that the swings travel 19mph. What is the diameter of the ride if the sign is correct?
 
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fluffertoes said:
Hello all! I need help with a certain type of problem. I do not know how I can find the diameter of a circular object given it's linear velocity. Here is an example problem, and I would love any explanation you could give me! Thanks! :))

Leaving the Ferris Wheel, Daniel sees his friend, Jenna, riding the Super Circle Swings. As he watches, she goes around 10 times in one minute. The sign on the ride claims that the swings travel 19mph. What is the diameter of the ride if the sign is correct?
Hint: [math]v = \omega r[/math]

How do you find [math]\omega[/math] ? I'd advised changing the 19 mi/h to ft/min.

-Dan
 
topsquark said:
Hint: [math]v = \omega r[/math]

How do you find [math]\omega[/math] ? I'd advised changing the 19 mi/h to ft/min.

-Dan

Oh my, are people ever going to switch to a system, not necessarily the metric system, that doesn't require a factor or divisor of, say, 88? (Wondering)
 
I like Serena said:
Oh my, are people ever going to switch to a system, not necessarily the metric system, that doesn't require a factor or divisor of, say, 88? (Wondering)

I really just don't know what to do...
 
Let's begin by taking the formula Dan provided, and solve for $r$:

$$r=\frac{v}{\omega}$$

Now, we know the radius $r$ is half the diameter $d$:

$$d=\frac{2v}{\omega}$$

We are given:

$$v=19\text{ mph}\cdot\frac{5280\text{ ft}}{1\text{ mi}}\cdot\frac{1\text{ hr}}{60\text{ min}}=1672\,\frac{\text{ft}}{\text{min}}$$

Now we need to turn 10 revolutions per minutes into an angular velocity given in radians (dimensionless) per minute:

$$\omega=10\,\frac{\text{rev}}{\text{min}}\cdot\frac{2\pi}{1\text{ rev}}=20\pi\,\frac{1}{\text{min}}$$

So, plug in these values...what do you get for $d$?
 
I like Serena said:
Oh my, are people ever going to switch to a system, not necessarily the metric system, that doesn't require a factor or divisor of, say, 88? (Wondering)
Hey, you're preaching to the choir. But, given the units, I figure the answer will be in ft.

-Dan
 
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