课程名称︰动力学 课程性质︰机械系必修 课程教师︰颜家钰 开课学院：工学院 开课系所︰机械系 考试日期（年月日）︰2010/6/22 考试时限（分钟）：120分钟(助教延长30分钟 共150分钟) 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : Choice (2 points each) 1. What is the assumption made when applying Newton's 2nd law to a system of particles ΣF_j = m_i a_i ,j=1,2,...,n. a) the measurements are based on a Newtonian frame, b) the particles are fixed together, c) the internal forces, f_ij does not act on the system particles, d) the particles does not interact among themselves. 2. A Newtonian frame refers to a frame that is a) moving at a constant acceleration, b) rotating at a constant angular velocity, c) moving at a constant speed, d) body fixed. 3. Consider a bug rests still on the disk rotating at angular speed ωk, were a is the vector point to B from the disk center and b is the vector pointing to P from the disk center. What is the velocity of the post, P, on the ground appear to the bug's eye, B? a) -ωk ×(b-a) b) -ωk ×b c) -ωk ×a d) ωk ×(b-a) 4. In problem 3, suppose the angular acceleration of the disk is αk, then what is the acceleration of the post, P, on the ground appear to the bug, B? a) αk ×a + ω^2 a b) αk ×b + ω^2 a - 2ωk ×(v_p)_rel c) αk × a + ω^2 a - 2ωk ×(v_p)_rel d) -2ωk ×(v_p)_rel 5. What is the difference between kinematics study and kinetic study a) kinematics study considers only the velocity of the motion, b) kinematics considers only the forces involved in the motion, c) kinetic study concerns the forces involved in the motion, d) kinetic study neglects the non-impulsive forces. 6. Consider applying a force F on the slide of mass m so that the slide is not moving. What can we say about the friction force, F_μ? a) F_μ = μ_k mg b) F_μ = F c) F_μ = μ_k N , N = -mg d) F_μ = μ_s mg 7. What is the assumption made on the forces acting on the ball, when applying conservation of angular momentum to the impact problem on the right? a) All the forces are parallel to the direction of motion, b) no particular assumption needed, c) there is no external forces other than the gravity, d) the ball sticks to the corner O after impact. 右图: ─────┐(球被卡在这里，O是接触点"┐"，球半径>阶差) 　　　 　 ///////////└───── /////////////////////////// 8. Consider the four point masses m connected by rigid massless bars of length l as shown in the right. What is the resulting acceleration when the force F is applied? (PS.长度是小写L，不是一) ○—○← l︱ ︱ F ○—○ a) F/4m b) F/2m c) F/2m + (l/2) ×(F/2m) d) none of the above. 9. In the above problem, what is the resultant angular acceleration α? a) F/2ml b) F/4ml c) Fl/4m d) none of the above. 10.To relate the applied moment ΣM_p with respect to point P in space with the change of angular momentum H_p for a system of particles, we can use . the relation ΣM_p = H_p when a) P is an arbitrary point b) P is any fixed point in space c) P is the location of the corner of the body. d) none of the above. 11.In the expression a_B = a_A + αk ×r_B/A - ω^2 r_B/A + (a_B)_rel + 2ωk ×(v_B)_rel , the term (a_B)_rel is commonly referred to as the a) Coriolis acceleration. b) the relative acceleration of point A to the body. c) the relative acceleration of point B to the body. d) the accelerationof point A. 12.Consider G is the mass center,ω is the angular velocity of the rigid body. For an arbitrary point P, which of the following statementsis true: _ a) H_P = H_G + r_G/P ×mv b) H_P = r_G/P ×m v_P + ∫r_/G ×(ω ×r_/G )dm c) H_P = r_G/P ×m v_P + ∫r_/P ×(ω ×r_/P )dm 13.Following the previous question, what is the assumption on P? a) P is the mass center b) P is a fixed point c) P is any arbitrary point d) P is an arbitrary point moving with the body. 14.Which on among the following quantity is not a vector? a) displacement, b) angular displacement, c) velocity, d) angular velocity. 15.What is the relationship between the moment of inertia of a body about its mass center, I^G and about another arbitrary point, I^P? a) I^P = I^G - mr^2, b) I^G = I^P - md^2, c) I^G = I^P + md^2, d) I^P = I^G Problems 16.(20%)The 1m-diameter disk shown in the figure has a mass of 20Kg. The mass center of the disk is located 250mm from the center of the disk, and its radious of gyration with respect to the fixed axis of rotation is 400mm. A cable wrapped around the circumference of the disk pass over a small pulley of neglible mass and is attached to a 25-Kg block B. If the disk has a counterclockwise angular velocity of 10 rad/s when θ= 0ﾟ. Write down the relation that determines the angle θ_m when the disk stops and begins to rotate clockwise. ┌───────────────────┬┬ │ ──────────────┤├╮ │ ↖此处与圆盘交 定滑轮位置→╰╯│ │ │ │ ■B │很难画的圆盘位置(转轴垂直纸面) ├─────╮ (质量分布不均) ├─────╯ │ │ ⊙ ←质心位置 │ │ ＼ 　 │ │ ＼ ╰ θ ╯ 17.(20%)The slender rod AB of length L forms an angle β with the vertical axis as it strikes the frictionless surface shown with a vertical velocity v_L and no angular velocity. Assuming that the impact is perfectly elastic, derive the expression for the angular velocity of the rod immediately after the impact. Moment of inertia of a slender rod about its mass center is (1/12)mL^2 . (本题试卷中L皆为小写，使用大写以方便与1区别) ╭β╮ ﹕ ∕B ﹕ ∕ ﹕ ∕ ﹕∕↓ v_L A∕ ──────────── 18.(30%)The 5kg uniform bar BDE is attached to the two rods AB and CD. Knowing that at the instant rod AB has an angular velocity of 6 rad/s clockwise and no angular acceleration, determine a) the velocity v_D,(10%) b) the acceleration a_D,(10%) c) the x-component of reaction force R_Bx at B.(10%) ─╮A ╭─╮ ◎╞════╪◎│B ─╯ 200mm │ │ │ │240mm │ │ ─╮C │ │ ◎╞══╪◎│D ─╯↑ │ │ 150mm │ │240mm │ │ │ │ │ │E ╰─╯ --

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