- #1
aeroegnr
- 18
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Ok, I'm using Beer and Johnston's engineering Mechanics/Dynamics book for class, and i don't particularly enjoy it's lack of explanation for the following problem:
The graphic shows a bullet flying to the right with the x coordinate pointing along its long axis and the y-axis perpendicular. The velocity is theta degrees below the x axis
"The 60-lb projectile shown has a radius of gyration of 2.4in. about its axis of symmetry Gx and radius of gyration of 10in. about the transverse axis Gy. Its angular velocity [tex]\omega[/tex] can be resolved into two components: One component, directed along Gx, measures the rate of spin of the projectile, while the other component, directed along GD, measures its rate of precession. Knowing that [tex]\theta[/tex]=5 degrees and the angular momentum of the projectile about its mass center G is Hg= (0.640 lb-ft-s)i - (0.018 lb-ft-s)j, determine:
a) the rate of spin
b) the rate of precession"
Now, the book provides no explanation of precession up to this point, and its absolutely driving me insane not knowing why the answer is what it is.
The answer in the back of the book for b is found by taking the j component of velocity [tex]\omega_\hat{j}[/tex] and then using this equation where [tex]\omega_\hat{p}[/tex] is the angular velocity in the direction of the moment of precession.
[tex]\omega_\hat{p}[/tex][tex]*sin(\theta)=\omega_\hat{j}[/tex]
The answer given in the back of the book for this therefore is .1596 rad/s.
I do not understand why this is so. The angular velocity in the y direction is
the farthest from the axis of precession, so why does it provide the only source of precession? Why does this precess and not just spin laterally and in horizontally at the same time?
If anyone can provide insight, I would be very thankful.
I also have more questions if you can answer this one.
The graphic shows a bullet flying to the right with the x coordinate pointing along its long axis and the y-axis perpendicular. The velocity is theta degrees below the x axis
"The 60-lb projectile shown has a radius of gyration of 2.4in. about its axis of symmetry Gx and radius of gyration of 10in. about the transverse axis Gy. Its angular velocity [tex]\omega[/tex] can be resolved into two components: One component, directed along Gx, measures the rate of spin of the projectile, while the other component, directed along GD, measures its rate of precession. Knowing that [tex]\theta[/tex]=5 degrees and the angular momentum of the projectile about its mass center G is Hg= (0.640 lb-ft-s)i - (0.018 lb-ft-s)j, determine:
a) the rate of spin
b) the rate of precession"
Now, the book provides no explanation of precession up to this point, and its absolutely driving me insane not knowing why the answer is what it is.
The answer in the back of the book for b is found by taking the j component of velocity [tex]\omega_\hat{j}[/tex] and then using this equation where [tex]\omega_\hat{p}[/tex] is the angular velocity in the direction of the moment of precession.
[tex]\omega_\hat{p}[/tex][tex]*sin(\theta)=\omega_\hat{j}[/tex]
The answer given in the back of the book for this therefore is .1596 rad/s.
I do not understand why this is so. The angular velocity in the y direction is
the farthest from the axis of precession, so why does it provide the only source of precession? Why does this precess and not just spin laterally and in horizontally at the same time?
If anyone can provide insight, I would be very thankful.
I also have more questions if you can answer this one.