Max Speed for 10 m Radius Spinning Drum Ride

[Alcape]

Homework Statement

If a spinning drum ride cannot exceed a 10 m radius, and the riders are not to
experience an acceleration greater than 2g, what is the maximum speed at
which the drum can spin?

Homework Equations

No Idea

The Attempt at a Solution

I tried using (theta) = tan^-1 of (rg/v²)
v² = (tan(theta))/(rg)
v = (root) of (tan(theta))/(rg)

 

[tiny-tim]

Hi Alcape!

(have a theta: θ )

If a spinning drum ride cannot exceed a 10 m radius, and the riders are not to
experience an acceleration greater than 2g, what is the maximum speed at
which the drum can spin?
…
I tried using (theta) = tan^-1 of (rg/v²)
v² = (tan(theta))/(rg)
v = (root) of (tan(theta))/(rg)

What's θ? You can assume that the drum's wall are vertical.

Now use the standard formula for centripetal acceleration ​

 

[Alcape]

If the walls are vertical then it doesn't work as it's at 90 degrees and tangent of 90 degrees then it comes out to be a mathematical error

 

[tiny-tim]

ah … you obviously haven't seen one of these at a fairground.

Yes, if the walls are smooth, it can't be done, but you can assume the walls are rough, so that friction will keep you up (or even that there's a ledge to stand on ).

 

[Alcape]

I now have the answer if you use the formula for acceleration:a=v²/r
and transpose it so that it becomes: v² = a*r and therefore becomes:
v = √(a*r) and it comes out to be 4.47...

 

[tiny-tim]

Hi Alcape!

(just got up :zzz: …)

I now have the answer if you use the formula for acceleration:a=v²/r
and transpose it so that it becomes: v² = a*r and therefore becomes:
v = √(a*r) and it comes out to be 4.47...

what about g ?

(and are you sure the question isn't asking for the angular speed?)

 

[Alcape]

Yes I'm sure as this is question a and b asks for the angle