04 Rigid.ppt

§4-1 刚体的运动 转动：刚体的各个质点都绕同一直线(转动轴)作圆周运动 在刚体上取一质元Pi： 刚体的转动动能 　 讨论：Jz的大小决定于 二、平行轴定理 三、薄板的垂直轴定理 一、刚体定轴转动的动量矩 　 若有n个外力作用，则 二、刚体定轴转动的动能定理 The broom balances at its center of gravity. If you saw the broom into two parts through the center of gravity and then weigh each part on a scale, which part will weigh the more? The short broom part is heavier. It balances the long handle just as kids of unequal weights can balance on a seesaw when the heavier kid sits closer to the fulcrum. Both the balanced broom and seesaw are evidence of equal and opposite torques - - not equal weights. (a)转动惯量大的滚得快 【练习】两个质量和半径都相同，但转动惯量不同的柱体，在斜面上作无滑动滚动，则： ? mg f R C x y (b)转动惯量小的滚得快 (c)滚得快一样快 (a)滚动情况不确定 √ 转动惯量小的滚得快！ 质心运动定理 过质心轴转动定理 纯滚动条件（运动学条件） Which will roll down a hill faster, a can of regular fruit juice or a can of frozen fruit juice? a) regular fruit juice b) frozen fruit juice c) depends on relative sizes and weights of cans The regular fruit juice has an appreciably greater acceleration down on incline than the can of frozen juice. Why? Because the regular juice is a liquid and is not made to roll with the can, as the solid juice does. Most of the liquid effectively slides down the incline inside the rolling can. The can of liquid therefore has very little rotational inertia compared to its mass. The solid juice, on the offer hand, is made to rotate, giving the can more rotational inertia. A pair of upright meter sticks, with their lower ends against a wall, are allowed to fall to the floor. One is bare, and the other has a heavy weight attached to its upper end. The stick to hit the floor first is the a) bare stick b) weighted stick c) …both the same Try it and see! In falling, both stick rotate about an axis at the lower end where the wall and floor meet. Their rate of rotation depends on their rotational inertias. The stick with the heavy weight at its upper end has more rotational inertia and is more lazy in rotating about it lower e