Re: [考試] 普物考古題

[ej41i6 (Sinon封王~)]

我把相簿裡的題目抄下來了.....

印出來討論應該比較方便吧.....

2002

１力場 F=Yi-Xj+Zk是否為保守力場？
２在質心靜止的座標觀察兩物體彈性碰撞，證明碰撞前後兩物體運動速度大小不變
３一多質點系統動能可以因在不同慣性座標而有不同，證明質心座標中所觀察到的動能為
最小值
４證明一多質點系統所受總力矩為其角動量對時間變化率，且總力矩不含內部相互作用所
產生之力矩
５一空心球殼，半徑Ｒ，質量Ｍ，求通過其質心知轉動慣量
６若重力加速度大小為ｇ，一圓柱體，質量Ｍ半徑Ｒ，由距地面ｈ處順著一斜坡　　　　　　　向下滾動但不滑動，求此圓柱體到地面時的速度大小
７舉一反例，說明角動量和角速度方向可能不平行
８A meter stick is held vertically with one end on the floor and is then
allowed to fall.Find the speed of the other end when it hit the floor, assuming
that the end on the floor does not slip.
９Two cylinders having radius R1 and R2 and rotational inertias I1 and I2 about
their central axis are supported by axles perpendicular to the plane of the
figure on the right.　The larger cylinder is initially rotating clockwise with
angular ω0 and. The small cylinder is moved to the right until it touches the
larger one and is caused to rotate by the frictional force between the two.
Eventually slipping ceases and the two cylinders rotate in the opposite direction.
(a)Is angular momentum or kinetic energy conserved? (b)Find the final angular
velocity ω2 of the smaller one in terms of  I1 I2 R1 R2 and ω0.
１０一靜止半球碗內面半徑R，一質點沿其無摩擦之碗內面水平射出，如此質點剛好可爬到
碗上邊緣，求質點初速Ｖ與與起始角度ψ的關係（起始角度：質點與球心連線與垂直線的
夾角）


2003


１三度空間運動之單一質點，證明外力對質點所作之功等於該質點增加的動能（須是三度
空間證明）
２一多質點系統動能可以因在不同慣性座標而有不同，證明質心座標中所觀察到的動能為
最小值
３在保守力場運動之質點如何定義其位能
４一圓柱體在一平面上滾動但不滑動，圓柱體和平面接觸之摩擦力是否作功
５一在向心力場F=f(r) r內運動之質點為何(a)其角動量為一常數向量(b)其軌道在一平面
上
６一均勻實心圓球半徑Ｒ質量Ｍ，證明通過質心之轉動慣量I=(2/5)(MR^2)
７對一轉動之剛體，證明K=(1/2)L．ω（注意兩者可能不平行）
８A rigid rod of length L and negligible mass has a ball with mass m attached
to one end and its other end fixed, to form a pendulum. The pendulum is
released at rest from a horizontal position. At what angle from the vertical
does the tension in the rod 　equal to the weight of the ball?
９A girl of mass M stands on a rim of a frictional merry-go-round of radius R
and rotational inertia I that us not moving. She throws a rock of mass m
horizontally in a direction that is tangent to the outer edge of the
merry-go-round. The speed of the rock, relative to the ground, is v.
Afterwards, what is the angular speed of the merry-go-round?
１０The rotational inertia of a collapsing spinning star change to 1/2 its
initial value. What is the ratio of the new rotational kinetic energy to the
initial rotational kinetic energy.

第7題L和ω上面都有向量符號
第5題F上面有向量符號右邊的r是單位向量


我抄的時候有稍微簡化一點點.....

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