MHB Find the diameter of a circle given linear velocity?

[fluffertoes]

[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?

 

[topsquark]

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

 

[I like Serena]

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)

 

[fluffertoes]

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...

 

[MarkFL]

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 $d$?

 

[topsquark]

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