课程名称︰ 中等动力学 课程性质︰ 选修 课程教师︰ 卢中仁 开课学院： 工学院 开课系所︰ 机械系 考试日期（年月日）︰ 97/4/25 考试时限（分钟）： 3节课 180分钟 是否需发放奖励金： 是 试题 : 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. 图片：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. (为了便於阅卷，请用图示的座标系，xyz 固定於AO上) 图片：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. 图片：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. (将结果表为固定於圆柱的座标 i-j-k ) 图片：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. 绕任意轴旋转的座标转换矩阵（[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 --

※ 发信站: 批踢踢实业坊(ptt.cc) ◆ From: 220.132.13.51