課程名稱︰ 中等動力學
課程性質︰ 選修
課程教師︰ 盧中仁
開課學院： 工學院
開課系所︰ 機械系
考試日期（年月日）︰ 97/4/25
考試時限（分鐘）： 3節課 180分鐘
是否需發放獎勵金： 是
試題 :
1. A cable that passes through a hole at point A is pulled inward at the
contant rate of 1 m/s, thereby causing the 0.2-kg collar to move along
the circular guide bar. The system is situated in the vertical plane.
Determine the speed and the rate of change of the speed of the slider at
the instant shown in the figure. Also evaluate the corresponding tension
in the cable.
圖片：http://www.wretch.cc/album/show.php?i=yaujack&b=3&f=1008619848&p=0
2. The sphere rolls without slipping over the interior wall of a hollow
cylinder that rotates about its axis at ω2. The angular speed of the
vertical shaft driving the sphere is ω1. Both rotation rates are
constant. Determine the angular velocity and angular acceleration of the
sphere. (為了便於閱卷，請用圖示的座標系，xyz 固定於AO上)
圖片：http://www.wretch.cc/album/show.php?i=yaujack&b=3&f=1008619849&p=1
3. The crank with a radius of 80mm turns with a constant angular velocity
ω0 = 4 rad/sec and causes the collar A to oscillate along the fixed
shaft. Determine the velocity of the collar A and the angular velocity
of the rigid-body link AB as the crand crosses the vertical position
shown.
圖片：http://www.wretch.cc/album/show.php?i=yaujack&b=3&f=1008619850&p=2
4. A reference frame xyz, initially coincident with the fixed reference
frame XYZ, is rotated through an angle β about axis n cap. The trans-
-formation from XYZ to xyz is [R]. For the specific transformation
[ 9 1 -3√2 ]
[R] = 0.1*[ 1 9 3√2 ]
[ 3√2 -3√2 8 ]
determine the corresponding rotation axis n cap and rotation angle β.
5. A test chamber for astronauts rotates about axis AB at a constant angular
speed ω1 as the entire assembly rotates about the horizontal axis at
angular speed ω2, which also is constant. An astronaut is seated
securely in the chamber at center point O, which is collinear with both
axes of rotation. Object C has a constant absolute velocity Vc parallel
to the horizontal axis. Determine the acceleration of this object as seen
by the astronaut. (將結果表為固定於圓柱的座標 i-j-k )
圖片：http://www.wretch.cc/album/show.php?i=yaujack&b=3&f=1008619852&p=3
％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％％
The following information may be useful for solving the question.
繞任意軸旋轉的座標轉換矩陣（[v]_xyz = [R][v]_XYZ）
[ R11 R12 R13 ]
R=[ R21 R22 R23 ]
[ R31 R32 R33 ]
R11 = n1^2(1-cosβ) + cosβ
R12 = n1n2(1-cosβ) + n3cosβ
R13 = n1n3(1-cosβ) - n2sinβ
R21 = n1n2(1-cosβ) - n3sinβ
R22 = n2^2(1-cosβ) + cosβ
R23 = n2n3(1-cosβ) + n1sinβ
R31 = n1n3(1-cosβ) + n2sinβ
R32 = n2n3(1-cosβ) - n1sinβ
R33 = n3^2(1-cosβ) + cosβ
. δA
A = —— + Ω×A , Ω is the angular velocity of the moving reference frame.
δt
Vp = Vo' + (Vp)_xyz + ω×Rp/o'
.
Ap = Ao' + (Ap)_xyz + ω×Rp/o' + ω×(ω×Rp/o') + 2ω×(Vp)_xyz
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