# Calculate RPM given the force of a torsion spring

• saaaaam
In summary, a flywheel of inertia has a torque of 0.667Nm when a torsion spring is released. The flywheel speed is maximised each time the torsion spring is at its relaxed position.

## Homework Statement

I've got a flywheel of Inertia = 0.0019302kg/m^2 (found via solidworks), when a torsion spring is released, a force of 10N acts on the wheel via astring attached 0.065m above and 0.0325m to the right of the wheel's axis at an angle of 40 degrees.

## Homework Equations

What is the flywheel's RPM (or rad/s or Hz)?

## The Attempt at a Solution

Torque produced = FhDv + FvDh = (10*sin(40))0.0325 + (10*cos(40))0.065
= 0.667Nm
Torque = Ia
a = Torque/I = 0.667/0.0019302
Am i lacking a length of time this torque is applied for? I struggle to se where to go from here[/B]

saaaaam said:

## Homework Statement

I've got a flywheel of Inertia = 0.0019302kg/m^2 (found via solidworks), when a torsion spring is released, a force of 10N acts on the wheel via astring attached 0.065m above and 0.0325m to the right of the wheel's axis at an angle of 40 degrees.

## Homework Equations

What is the flywheel's RPM (or rad/s or Hz)?

## The Attempt at a Solution

Torque produced = FhDv + FvDh = (10*sin(40))0.0325 + (10*cos(40))0.065
= 0.667Nm
Torque = Ia
a = Torque/I = 0.667/0.0019302
Am i lacking a length of time this torque is applied for? I struggle to se where to go from here[/B]
I di don't check your numbers but the approach looks good . Note that ##\alpha## is in rad/s^2. To get to your question, I am puzzled too. It is not possible to calculate an RPM without more information. For example the amount of time it was applied, as you said (and then we would need to know if the direction of the force changes as the wheel rotates, and if so how it does). There is really no other information provided?

This is actualy the analysis of a project I've made, so yes there is no other information i can add to it. I'm thinking i'll time the flywheels motion after activation and just count the revolutions... i was just hoping there was a theory based way to calculate it! thanks for the reply

saaaaam said:
This is actualy the analysis of a project I've made, so yes there is no other information i can add to it. I'm thinking i'll time the flywheels motion after activation and just count the revolutions... i was just hoping there was a theory based way to calculate it! thanks for the reply
Since it is a torsion spring the torque will not be constant. In principle you have an SHM oscillator. The flywheel speed will be maximised each time the torsion spring is at its relaxed position. So what you need to know is the energy initially stored in the spring.
But that is ignoring practical considerations of friction and drag.

## 1. How do I calculate the rotational speed (RPM) of a torsion spring given the applied force?

To calculate the RPM of a torsion spring, you will need to know the force applied to the spring and its moment of inertia. The formula for calculating RPM is: RPM = (force / moment of inertia) * 60. Make sure to convert the units of force and moment of inertia to the appropriate units before plugging them into the formula.

## 2. What is the moment of inertia and how does it affect the RPM calculation for a torsion spring?

The moment of inertia is a measure of an object's resistance to rotational motion. In the case of a torsion spring, it is a measure of how difficult it is to rotate the spring around its axis. The higher the moment of inertia, the lower the RPM calculation will be for a given force.

## 3. Can I use the same formula to calculate the RPM of any torsion spring?

Yes, the formula for calculating RPM is universal and can be applied to any torsion spring as long as you have the necessary information about the applied force and the spring's moment of inertia. However, keep in mind that the units of force and moment of inertia may vary depending on the specific system of measurement being used.

## 4. How accurate is the RPM calculation for a torsion spring?

The accuracy of the RPM calculation depends on the accuracy of the measurements taken for the force and moment of inertia. Additionally, the formula assumes that the spring is being rotated in a uniform manner, which may not always be the case in real-world scenarios. It is always best to double-check your calculations and make adjustments as needed.

## 5. Are there any other factors that can affect the RPM of a torsion spring besides the applied force and moment of inertia?

Yes, there are other factors that can affect the RPM of a torsion spring, such as the material and shape of the spring, the temperature, and any external forces acting on the spring. These factors may alter the spring's behavior and should be taken into consideration when calculating RPM.