Toy Gyroscope Problem: Finding Angular Speed and Upward Force | Homework Help

[EvanQ]

Homework Statement

The rotor (flywheel) of a toy gyroscope has mass 0.140 kilograms. Its moment of inertia about its axis is 1.20x10^{-4} kilogram meters squared. The mass of the frame is 0.0250 kilograms. The gyroscope is supported on a single pivot with its center of mass a horizontal distance 4.00 centimeters from the pivot. The gyroscope is precessing in a horizontal plane at the rate of one revolution in 2.20 seconds.

Find the upward force exerted by the pivot.

Find the angular speed omega at which the rotor is spinning about its axis, expressed in revolutions per minute.

Homework Equations

angular momentum and acceleration equations eg:
w = O / t
w= w0 + at
O = w0t + ½ at^2
w^2 = w0^2 + 2aO

The Attempt at a Solution

having a lot of trouble determining what information is relevant in this question...very little idea how to go about it sorry.

i think it has to do with L = Iw, with I being 1.2x10^4, but I'm unsure of how to get the angular velocity, and after that the force they are asking for.

 

[Astronuc]

Try this reference for the various equations and variables

http://hyperphysics.phy-astr.gsu.edu/hbase/mi.html

http://hyperphysics.phy-astr.gsu.edu/hbase/rotv.html
http://hyperphysics.phy-astr.gsu.edu/hbase/rotv2.html

Write out the variables given and their values.

 

[theperthian]

PCB250??
bahahaha
now guess why I am here...

 

[danni7070]

You will have to change (Big Omega) O from rev/2.2s into rad/s : O = 2pi/2.2s = 2.856 rad/s.
The upward force is equal to the weight because the gyroscope is not moving sideways, up or down so Fx = 0, and Fy = 0. Hence n = w = (m_rotor + m_frame)*9.8.

We know that O = T/L (where Torque: T = radius * w and L = I * w (small omega))

I is given with 1.2E^-4 kg*m^2.

There's an equation that tells you that L = I*w here so you just have to find the L from the equations above and then isolate w(small omega) from L = I * w(small omega).

then you'll get some number but you will have to answer in rev/min and remember that O is given in rev/2.2s but you changed it to 2.856rad/s

I have to admit that I'm in trouble finding the answer in rev/min if somebody could point out the right way to do so.

 

[theperthian]

well evanQ, guess who had two attempts left when doing that. then i got the right answer! but it wasnt it revolutions per minute. so i had to convert it...and i MULTIPLIED BY 60 INSTEAD OF DIVIDED! ahhh! soooooo annoyed.

anywho, that's all in the past...now there another one to worry about. where we get marks taken off for getting multichoice wrong, nooooooo