Science > Physics > Calculating force required to accelerate (rotate) a disk
| Topic: |
Science > Physics |
| User: |
"Randy MacKenna" |
| Date: |
07 Feb 2005 08:29:23 PM |
| Object: |
Calculating force required to accelerate (rotate) a disk |
Okay...this is going to be another simple force question (I hope :-)...
If I have a solid steel shaft directly coupled to an electric motor,
how do I figure out how much torque the motor has to produce in order
to get the shaft to spin at a certain RPM, within a certain amount of
time?
For example, if I have a solid shaft that is 50cm in diameter, and it
has a mass of 30Kg -- how much force is required to get it to spin at a
rate of 1000 RPM within 5 milliseconds? We can assume zero friction.
I'm very interested in learning how to set up and solve such equations
on my own, so as much explanation as you are inclined to give would be
*greatly* appreciated.
Thanks!
Randy M
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| User: "Timo Nieminen" |
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| Title: Re: Calculating force required to accelerate (rotate) a disk |
07 Feb 2005 09:42:47 PM |
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On Tue, 7 Feb 2005, Randy MacKenna wrote:
Okay...this is going to be another simple force question (I hope :-)...
If I have a solid steel shaft directly coupled to an electric motor,
how do I figure out how much torque the motor has to produce in order
to get the shaft to spin at a certain RPM, within a certain amount of
time?
For example, if I have a solid shaft that is 50cm in diameter, and it
has a mass of 30Kg -- how much force is required to get it to spin at a
rate of 1000 RPM within 5 milliseconds? We can assume zero friction.
I'm very interested in learning how to set up and solve such equations
on my own, so as much explanation as you are inclined to give would be
*greatly* appreciated.
I think the easiest way to learn how to do simple rotation problems like
this is to realise that they're almost identical to problems involving
motion in a straight line.
OK, if you were asking how much force is required to accelerate an object
(say of mass 10 kg) to a particular speed (say 100 m/s) is a specified
time (say 5 ms), then you would think (force times time) = change in
momentum,
and write
F * 0.005 = 10 * 100
F = 200,000 N
Now, your rotational motion problem is almost exactly the same! Substitute
torque for force, moment of inertia for mass, and angular velocity for
velocity.
torque x time = I x angular_velocity
and to go further, you need to know the moment of inertia I. This you will
either look up in a table, or if you're keen on integration, you can
find it yourself. Note that the contribution to the momentum of inertia of
a small mass element dm at a distance r from the axis of rotation is
dI = dm r^2
and dm = density x dV, where dV is a volume element.
dV = dx dy dz, but it's probably more convenient to use cylindrical
coordinates r,phi,z so dV = r dr dz dphi.
Anyway, this will give you the torque. If you need to convert this to a
force applied to the outside of the solid shaft, just remember that torque
= force x distance. (OK, what distance? Draw a diagram. Axis about which
the rotation happens, point at which force is applied, direction of force.
How long is the line from the rotation axis to a line along the force,
where there is a right angle between these two lines? Handy with vectors?
Just find the cross product!)
--
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html
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| User: "PD" |
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| Title: Re: Calculating force required to accelerate (rotate) a disk |
07 Feb 2005 09:39:38 PM |
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Randy MacKenna wrote:
Okay...this is going to be another simple force question (I hope
:-)...
If I have a solid steel shaft directly coupled to an electric motor,
how do I figure out how much torque the motor has to produce in order
to get the shaft to spin at a certain RPM, within a certain amount of
time?
For example, if I have a solid shaft that is 50cm in diameter, and it
has a mass of 30Kg -- how much force is required to get it to spin at
a
rate of 1000 RPM within 5 milliseconds? We can assume zero friction.
Wow, a big wonking torque that would be.
I'm very interested in learning how to set up and solve such
equations
on my own, so as much explanation as you are inclined to give would
be
*greatly* appreciated.
Analogous to F = m*a,
Write torque = (moment of inertia) x (angular acceleration)
For a solid disk, moment of inertia = (1/2) x M x R^2
Angular acceleration you're going to want in radians per second per
second.
Convert 1000 rpm into radians per second to start. You want to go from
0 to that number of radians per second in 0.005 seconds. You can figure
out whether to multiply or divide by dimensional analysis.
Thanks!
Randy M
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