# Spinning around a cylinder with a person inside

• Mathman23
In summary, Fred is trying to find the maximum period of revolution necessary to keep a person from falling from an amusement park ride. He starts by drawing a force- diagram and finds that the only radial force acting on the person is the normal force from the wall. He then solves for the radial force, the angular velocity, and the period.
Mathman23
Hi I have physics problem which I'm stuck with.

It goes like this.

An amusement park ride consists of a large vertical cylinder that spins around its axis fast enough for any person inside is held up against the wall then the floor drops away. The coefficient of static friction is $\mu_{s}$ and the radius of the cylinder is R.

I'm suppose to show the following: The maximum period of revolution necssary to keep the person from falling is $T = \frac{(4 \pi^{2} R \mu_{s})}{g}^{1/2}$

I know that in order to understand the situation I first need to draw a force-diagram displaying the forces acting on both the cylinder and the person inside.

Do I add these forces together then?

Any help/hint(s) will be appreciated :-)

Sincerley

Fred

No, you don't need to add all forces together. Just break into vertical and horizontal (radial) components. Identify the three forces that act on the person and solve for the radial force, then for the angular velocity, and hence for period.

Then the forces acting on the person and cylinder must be $f_{s} = \mu_{s} \cdot n$ , $F_{g} = m \cdot g$ , $F_{z} = m \cdot a$

Since it turns around the Z-axis I guess $F_{x} = 0$ $F_{y} = 0$.

I know both the cylinder and person are affect by acceleration too $a_{c} = m \frac{v^{2}}{r}$

The component forces are then:

$F_{\textrm{person} }} = m \cdot g + \mu_{s} \cdot n$??

$F_{\textrm{cylinder}} = m \cdot g + m \cdot \frac{v^2}{r}$??

Sincerely

Fred

ramollari said:
No, you don't need to add all forces together. Just break into vertical and horizontal (radial) components. Identify the three forces that act on the person and solve for the radial force, then for the angular velocity, and hence for period.

Mathman23 said:

Then the forces acting on the person and cylinder must be $f_{s} = \mu_{s} \cdot n$ , $F_{g} = m \cdot g$ , $F_{z} = m \cdot a$

You didn't observe that the normal force the wall applies on the person is the only radial force, so n = ma, and thus

$$f_s = \mu_{s}ma = \mu_{s}m\omega ^2r$$

On the other hand, f_s must balance the person's weight G.

Therefore,

$$f_s = mg$$

$$\mu_{s}m(\frac{2\pi}{T})^2r = mg$$

or,

$$\mu_{s}\frac{4\pi ^2}{T^2}r = g$$

or,

$$T = \frac{\sqrt{4\pi ^2\mu_{s}r}}{g}$$

Mathman23 said:
Since it turns around the Z-axis I guess $F_{x} = 0$ $F_{y} = 0$.

That is not the case. The centre of mass of the cylinder is not moving in the x or y direction, but the person is accelerating in the horizontal (radial) direction, so that F_x is not zero. F_y, yes is zero.

Regards,
Ervin

Just a minor comment: the g should go under the root sign:

$$T=2\pi \sqrt{\frac{\mu_s R}{g}}$$

Galileo said:
Just a minor comment: the g should go under the root sign:

$$T=2\pi \sqrt{\frac{\mu_s R}{g}}$$

That looks much better, but I tried to reach the expected answer.

## 1. How does spinning around a cylinder with a person inside affect their body?

Spinning around a cylinder with a person inside can have various effects on their body, depending on factors such as the speed of rotation and the size of the cylinder. The centrifugal force generated by the rotation can cause dizziness, nausea, and disorientation. It can also put strain on the muscles, joints, and cardiovascular system.

## 2. What happens if the person inside the cylinder is spinning too fast?

If the person inside the cylinder is spinning too fast, the centrifugal force exerted on their body will increase, potentially causing more severe symptoms such as loss of consciousness or muscle fatigue. It is important to monitor the speed of rotation and make sure it does not exceed the body's limits.

## 3. Can spinning around a cylinder with a person inside have any long-term effects?

Spinning around a cylinder with a person inside can have long-term effects on their body if done frequently or at high speeds. It can lead to changes in the inner ear, which can affect balance and coordination. It can also cause muscle strain and joint problems if not done properly.

## 4. How does gravity play a role in spinning around a cylinder with a person inside?

Gravity plays a crucial role in spinning around a cylinder with a person inside. It is the force that keeps the person in place inside the cylinder and prevents them from flying out due to the centrifugal force. Without gravity, it would be impossible to spin around a cylinder without the person floating away.

## 5. Is it safe for anyone to spin around a cylinder with a person inside?

No, it is not safe for everyone to spin around a cylinder with a person inside. The intensity and speed of the rotation can have different effects on different individuals, depending on their age, health, and physical condition. It is important to consult with a medical professional before attempting to spin around a cylinder with a person inside, and to always do so under proper supervision and with caution.

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