8.2 角动力

Section outline

• Select section General

  Collapse Expand

  General

  Collapse all Expand all

  • Select activity 新闻通告

    

    新闻通告 Forum
• Select section 角动

  Collapse Expand

  角动

  

  播放段落

  So what makes an object more difficult to turn? 
  ::那么,是什么使物体更难转弯呢?

  播放段落

  The difficulty it requires to push an object through space is called or more precisely translational inertia.  Inertia is equal to mass.  The difficulty required to turn an object is called rotational inertia or sometimes “moment of inertia”.  This is symbolized by the letter $\begin{array}{r}I\end{array}$ (for inertia). 
  ::将一个物体推进太空所需的困难被称为或更精确地称为翻译惯性。 惯性等于质量。 转换一个物体所需的困难称为旋转惯性, 有时称为“ 惯性运动 ” 。 这用字母I( 惯性) 表示。

  播放段落

  Try this out.  Take a long object like a broomstick or baseball bat.  Lay it flat and try to spin it with one hand.  This can be difficult.  Now instead, stand it upright and just give a twist with your fingers to turn it around.  The same object is more difficult to spin one way than the other.    Rotational inertia depends on both the mass and the mass distribution of an object. Mass closer to the axis is easier to turn.  Mass farther from the axis is harder to turn.
  ::试一下这个。 拿一个像扫帚或棒球棒这样的长的物体。 平放它, 并试图用一只手旋转它。 这可能是困难的。 相反, 站直它, 用手指扭转它。 同一个物体比其他物体更难旋转。 旋转性惯性取决于物体的质量与质量分布。 接近轴的重量比较容易旋转。 远离轴的重量比较难旋转。

  播放段落

  Angular is defined as how quickly an object is turning, and is symbolized by the Greek letter omega: $\begin{array}{r}\omega \end{array}$ .  In physics , angular velocity is generally measured in one of two units:
  ::角被定义为物体转动的速度,以希腊字母 omega 表示: 。在物理学中,角速度一般用两个单位之一测量:

  播放段落
  • Revolutions per second, or $\begin{array}{r}\text{rev/s}\end{array}$ .  A complete rotation or revolution is equivalent to motion through 360-degrees. An object that turns around 30 times in one minute has an angular velocity of 0.5 rev/s. 
    ::每秒发生革命,或变异/秒。完全旋转或革命等于通过360度运动。一个在一分钟内旋转30次的物体角速度为0.5瑞弗/秒。
  播放段落
  • Radians per second or $\begin{array}{r}\text{rad/s}\end{array}$ .  A radian is the around the edge of a circle of radius 1.  It takes $\begin{array}{r}2\pi \end{array}$ radians to complete one circle, so $\begin{array}{r}2\pi -\end{array}$ radians are equivalent to 1 revolution (360 degrees).
    ::弧度每秒或弧度/秒。弧度是半径1圆边缘的周围。 弧度需要 22 弧度才能完成一个圆, 所以 2 radians 等于 1 革命( 360 度) 。

  播放段落

  Use the simulation below to learn more about how a balancing pole can increase the rotational inertia of a tightrope walker and decrease his angular around the rope:
  ::使用下面的模拟来了解更多关于平衡杆如何能增加绳索行走器的旋转惯性并减少绳索周围的角角:

  播放段落

  Linear is defined as the product of mass and linear velocity $\begin{array}{r}(p=mv)\end{array}$ .  In the same way, angular momentum is defined as the product of rotational inertia and angular velocity .   The formula for angular momentum is stated as:
  ::线性被定义为质量和线性速度(p=mv)的产物。同样,角动量被定义为旋转惯性和角性速度的产物。角动量的公式如下:

  播放段落

  $\begin{array}{r}L=I\omega \end{array}$
  ::L=I

  播放段落

  where $\begin{array}{r}I\end{array}$ is the rotational inertia (a term related to the distribution of mass) and the Greek letter omega $\begin{array}{r}\omega \end{array}$ is the angular velocity.  Just like momentum in a given direction, objects undergoing rotation obey a similar conservation principle called conservation of angular momentum, which can be expressed as $\begin{array}{r}{I}_i{\omega }_i=I_f{\omega }_f\end{array}$ .
  ::我指的是旋转惯性(一个与质量分布有关的术语)和希腊字母 omega {} 是角速度。 就像在特定方向上的势头一样, 正在旋转的物体也遵循类似的保护原则, 称为角动力保护, 可以用 Iii=IFf 表示 。

  播放段落

  An important difference is that in linear momentum, the inertia is always the same.  In angular momentum, the rotational inertia $\begin{array}{r}I\end{array}$ and the angular velocity $\begin{array}{r}\omega \end{array}$  can change.  Perhaps you’ve noticed that when a spinning figure skater pulls in her arms close to her body, her rotational velocity increases. Or perhaps you’ve seen a high driver spring off the diving board, tuck his legs close to his body, and spin quickly. What’s going on? In each case the person brings more of their mass closer to the axis about which their body spins. The result is that their angular velocity increases.
  ::一个重要的区别是线性动力,惯性总是一样。在角性动力中,旋转性惯性I和角性速度可以改变。也许你已经注意到,当旋转式滑冰者拉动她的手臂接近她的身体时,她的旋转速度会加快。 或者你已经看到一个高驾驶员跳下潜水板,把腿拉近他的身体,并快速旋转。 发生了什么事情?在每一种情况下,一个人将更多的质量带到他们身体旋转的轴上。结果就是他们的角速度加快了。

  播放段落

  The conservation of angular momentum ensures that, should the mass in the system move closer to the axis of rotation, the system will spin (rotate) more quickly. A classic demonstration of the conservation of angular momentum is shown in the following video .  As the student in the figure moves the inward toward his body, his angular velocity increases, but his angular momentum stays constant.
  ::保持角动力可以确保,如果系统质量更接近旋转轴,系统将更快旋转(旋转 ) 。 以下视频显示了角动力保护的典型表现。 当图中的学生向身体内移时,他的角速度会加快,但角动力会保持不变。

  播放段落

  Further Reading
  ::继续阅读

  播放段落

  Summary
  ::摘要

  播放段落
  • The angular momentum of an object is the product of rotational inertia and angular velocity.
    ::物体的角动量是旋转惯性和角速度的产物。
  播放段落
  • The angular velocity of an object is how quickly an object is turning.
    ::对象的角速度是物体转动的速度。
  播放段落
  • The rotational inertia is the difficultly required to turn an object.
    ::旋转惯性是旋转对象的难度所在。

  播放段落

  Review
  ::回顾

  播放段落
  1. You have two coins; one is a standard U.S. quarter, and the other is a coin of equal mass and size, but with a hole cut out of the center.
     播放段落
     1. Which coin has a higher moment of   ?
        ::哪个硬币有更高的时刻?
     播放段落
     2. Which coin would have the greater angular momentum if they are both spun at the same angular   ?
        ::哪个硬币的角力更大? 如果两者都在同一角上旋转,那么哪个硬币的角力会更大?
     
     ::你有两个硬币;一个是标准的美国季度,另一个是质量和大小相等的硬币,但有一个洞从中间切开。哪个硬币有更高的时刻?如果两个硬币都在同一角旋转,哪个硬币的角动力会更大?
  播放段落
  2. A star is rotating with a period of 10.0 days. It collapses with no loss in mass to a white dwarf with a radius of   $\begin{array}{r}.001\end{array}$   of its original radius.
     播放段落
     1. What is its initial angular   ?
        ::最初的角是什么?
     播放段落
     2. What is its angular velocity after collapse?
        ::塌陷后的角速是多少?
     
     ::恒星在10天的周期内旋转。 它向原半径为0.001 半径的白矮星倾斜, 其质量没有损失。 它最初的角是什么? 它在崩溃后的角速度是多少 ?
  播放段落
  3. A merry-go-round consists of a uniform     disc of   $\begin{array}{r}225\mathrm{k}\mathrm{g}\end{array}$   and a radius of   $\begin{array}{r}6.0\mathrm{m}\end{array}$ . A single   $\begin{array}{r}80\mathrm{k}\mathrm{g}\end{array}$   person stands on the edge when it is coasting at   $\begin{array}{r}0.20\end{array}$   revolutions per sec. How fast would the device be rotating after the person has walked   $\begin{array}{r}3.5\mathrm{m}\end{array}$   toward the center. (The moments of     of     objects add.)
     ::旋转木马由1个225公斤和半径6.0米的统一圆盘组成。 单80公斤的人站在边缘,在每秒0.20次翻转时处于边缘。 在该人向中心行驶3.5米之后,该装置的旋转速度有多快。 (物体的瞬间添加 。)

  播放段落

  Explore More
  ::探索更多

  播放段落
  1. 播放段落

     The system pictured in the video above (which includes the student, weights, and spinning seat) has an initial rotational inertia  $\begin{array}{r}{I}_i\end{array}$  and an initial angular velocity  $\begin{array}{r}{\omega }_i\end{array}$   2.00 rev/s. After the student pulls the weights toward his chest, the final rotational inertia of the system is only 80% of its initial rotational inertia- that is  0.800  $\begin{array}{r}{I}_i\end{array}$ .
     ::以上视频中描述的系统(包括学生、重量和旋转座椅)有一个初始旋转惯性Ii和初始角速度i 2.00 rev/s。在学生将重量拉到胸前后,这个系统的最后旋转惯性只占其初始旋转惯性(即0.800 Ii)的80%。

     Assuming that the angular momentum of the system is conserved, what is the final angular velocity of the system?
     ::以上视频中所描绘的系统(包括学生、重量和旋转座椅)具有初始旋转惯性Ii和初始角速度 i 2.00 rev/s。在学生将重量拉到胸部后,系统的最后旋转惯性仅为其初始旋转惯性(即0.800 Ii)的80%。假设系统角动力得到保存,系统的最后角速度是什么?