ES480 3D Dynamic and Gyroscopic Motion
Dynamic and Gyroscopic Motion
Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: THEend8_
ES480 3D Dynamic and Gyroscopic Motion
Problem 1
The slender bar of length l and mass m is
rigidly attached to a shaft which is free to
turn with constant angular velocity in the
two bearings as indicated. The y and y
axes point into the page at the mass center
C. Determine the moment about the mass
center C supplied by the shaft to disk.
Answer:
2 2
sin cos
12
Cy
ml
M
In addition, (1) evaluate the reaction forces
in the bearings A and B, (2) judge whether
the proper dynamic balance should be
made in the sense M or N.
Problem 2
The uniform slender bar of mass per
unit length is freely pivoted about the
y-axis at the clevis, which rotates about the
fixed vertical z-axis with a constant
angular velocity . Determine the
steady-state angle assumed by the bar,
length b is greater than length c.
Answer:
2 2
1
2 3 3
3
sin
2
g b c
b c
Problem 3
The large satellite-tracking antenna has a
moment of inertia I about its z-axis of
symmetry and a moment of inertia OI
about each of the x-axis and y-axis.
Determine the angular acceleration of
the antenna about the vertical Z-axis
caused by a torque M applied about Z by
the drive mechanism for a given
orientation .
Answer:
2 2cos sinO
M
I I
Problem 1
Problem 2
Problem 3
ES480 3D Dynamic and Gyroscopic Motion
Problem 4
The disk is pinning about the slight axel
and the whole assembly precesses about
the vertical axis with constant rate 32
rad/s. If the axel is observed to remain
horizontal, find the magnitude and the
direction of the spin of the disk.
Answer.
30.7 /rad s about +z axis
Problem 5
The slender rod OA of mass m and length l
rotates freely about a horizontal axis
through O. The pivot at O and attached
shaft rotate with a constant angular
velocity about the vertical z-axis. Write
the expression for the angle assumed
by the rod. What minimum value must
attain before the rod will assume other than
a vertical position.