2001.11.13.
1.Please write down the three Newton's laws of motion in both translational
and angular forms,including their "equivalent" expressions (等價表達) of
Newton's second law. What are the assumptions for their application in
classic mechanics? Are those "equivalent" forms really equivalent? Why?
(20%)
2.Please derive the two equivalent angular forms of the Newton's Second law
from the corresponding translation forms.
(10%)
3.Please prove the parallel-axis theorem and calculate the rotational
inertia of body (a) (b) (c) (d)
說明:有附圖,我把大致的說明一下
(a)是solid cylinder(or disk)about central axis半徑R,柱高L,柱面圓心是
中心軸
(b)是solid cylinder(or disk)about axis through one end perpendicular
to length圖形及符號跟(a)同,只是軸在柱一端圓面某直徑上
(c)solid sprere about any diameter球直徑2R,軸與球相切
(d)slab about the axis長a寬b的矩形面(高不重要),軸在a邊上
(25%)
4.A wheel id rotating freely with an angular speed of 10 rev/s about an axis
whose rotation inertia is negligible. A second wheel,initially at rest and
with twice the rotational inertia of the first,is suddenly coupled to the
same axis.
(a)What is the angular speed of the resultant combination of the axis and
two wheels?
(b)What fraction of the original rotational-kinetic energy is lost?
(20%)
5.The rotational inertia of a collapsing spinning star changes to one-fourth
its initial value. What is the ratio of the final angular momentum and
rotational kinetic energy to the initial ones?
(10%)
6.a round uniform body(圓盤) of mass M and radius R rolling down a ramp at
an angle thita(打不出來). (原題目有附圖)
(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?
(15%)
7.Good luck!!!!
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