Calculate RPM given the force of a torsion spring

[saaaaam]

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
= 345.5 rad/s(?)
Am i lacking a length of time this torque is applied for? I struggle to se where to go from here[/B]

 

[nrqed]

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
= 345.5 rad/s(?)
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?

 

[saaaaam]

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

 

[haruspex]

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.