普物期中考考古題（林敏聰） 20.Nov.2003

[Steggie (p2新板Tread_softly)]

（驚）我又發現了 2003 的.......

不過內容又是大同小異！！
這樣應該很好抓重點是什麼了吧（茶）
現在大家有三份考古題了，祝大家都能考很好喔 ˋ( ° ▽°)ˊ

我把前兩份沒出現的題目的題號用黃色標起來。

1. (25%)
   (a) Please write down the three Newton's laws of motion in both
       translational and angular forms, including their "equivalent"
       expressions of Newton's second law.
   (b) What are the assumptions for their application in classic mechanics?
   (c) Are those "equivalent" forms really equivalent?
   (d) Please prove the two equivalent expressions of Newton's second law in
       angular forms from those in translational form.

2. (15%) Please prove the parallel-axis theorem and calculate the rotational
   inertias of body (a), (b), (c), and (d) (see Fig.1)

   Fig.1
   (a) Solid cylinder about central axis
       圓柱，半徑 R，長 L，轉軸過柱面圓心，平行於 L
   (b) Solid cylinder (or disk) about the indicated axis
       圓柱，半徑 R，長 L，轉軸過底面的邊緣，垂直於 L
   (c) Solid sphere about any diameter
       圓球，半徑 R，轉軸過球心
   (d) Slab about perpendicular axis through center
       矩形板子，長 a，寬 b，轉軸垂直於板面，過其中一個頂點

3. (15%) Fig.2 shows a round uniform body of mass M and radius rolling down
   a ramp at angle θ.
  (a) What is the linear acceleration of the rolling body?
  (b) What is the friction force fs（s 下標）?
  (c) What is the speed of the rolling body at the bottom if the ramp has
      length L?

  Fig.2 懶得畫了，應該從題目就看得懂了吧

4. (15%) Consider a damped simple harmonic motion with the total force
   ΣF = - kx - bv, where k is force constant of the spring, x the
   displacement, v the velocity, b the damping constant. Please write down
   and solve the (differential) equation of motion from the Newton's second
   law.

5. (15%) Two blocks and two springs with spring constant k are arranged on a
   horizontal, frictionless surface as shown in Fig.3. The coefficient of the
   static friction between the two blocks is μ. What is the maximum possible
   amplitude xm（m 下標）of simple harmonic motion of the spring-
   blocks system if no slipping is to occur between the blocks?

   Fig.3    |     m      |
            |  k  □  k  |
            |~~~~~□~~~~~|
            |     M      |

6. (15%) Please show that the total (internal) torque in an isolated system
   (i.e. without external torque and force) of many particles which act on
   each other with force Fij（i, j 下標）is zero.

7. Good luck!!

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請推 大家期中考都會嗨趴 ^^

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推 gwava:真好心有好報....妳的好心   鄭先生有看到
推 gwava:這樣更顯得答案的重要....背答案....
推 geniusjazz:大家期中考都會嗨趴 ^^
推 gwava:     大家期中考都會嗨趴 ^^
推 dQoQb:超讚~謝囉
推 xiphoarch:除了推還是推啊啊啊啊啊啊啊~~~XD
推 yiba:好心會有好報的.你做的事 蘇先生都有看到
推 Jyou:      大家期中考都會嗨趴 ^^
推 pluss:     大家期中考都會嗨趴 ^^
推 knightwww:感謝啊
推 chaogold:第七提依樣
推 davidtea:............
推 xiphoarch:第7題一樣...所以沒有標黃色啊 (認真貌)
推 Steggie:樓上的說出了我標黃色時的心聲 XDD