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課程名稱︰普通物理學甲上
課程性質︰大一必修
課程教師︰林敏聰
開課學院：理學院
開課系所︰物理系
考試時間︰95.11.23
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1.(15%)Please write down the three Newton's laws of motion in both translation
and angular forms,including their "equivalent" expressions of Newton's
second law.What are the assumptions for their application in classic
mechanics?Are those "equivalent" forms really equivalent?Why?
2.(20%)Please prove the parallel-axis theorem and calculate the rotational
inertia of body (a),(b),(c)(see Fig.1)
3.(10%)A thin uniform rod,with length L and mass M,laid still on the desk,was
hit by a small mass m with velocity v,as shown in Fig.2.The mass sticks to
the rod end after collision and the friction can be neglected.What's the
linear velocity of the mass center just after collision and what is the
angular velocity of the composite system with respect to it?
4.(10%)A small ball,with mass m,radius r,is initially held still on the top of
a semi-sphere,radius R,and starts to roll down(without sliding all the way)
from top.At what angle the ball will leave the surface if(a)the semi-sphere
is fixed on the ground?
Or(10%)(b)the semi-sphere is on a frictionless ground?
5.(10%)A system consists of N particles mi,each with velocity vi and position
vector ri.Assuming the interaction between particles are all central forces,
please prove that the external torque τext=dLsys/dt,where Lsys is the total
angular momentum of the system.
6.(15%)A small mass m is released from a distance H above the ground,and then
hits and sticks to a block connected with a spring,spring constants K,
uncompressed length L0,to another block rest on the ground,see figure 4.
What's the minimum H for the whole system to leave the ground when the mass
bounces back?Assume the dimension of the block can be ignored.
7.(10%)An uniform solid cylinder rolls down a ramp smoothly(without sliding)
at angle θ.(a)What is the acceleration of the body's center of mass?(b)
Find the minimum coefficient of static friction at which the slide would not
happen.
8.(10%)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 Newton's Second Law.
9.Good luck!!!
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