[問題] 普物一題

[deepwoody (快回火星吧)]

A spool of thread consists of a cylinder of radius R1 with end caps of radius

R2 as shown in the end view illustrated in Figure P10.77. The mass of the

spool, including the thread, is m, and its moment of inertia about an axis

through its center is I. The spool is placed on a rough horizontal surface so

that it rolls without slipping when a force T acting to the right is applied

to the free end of the thread. Show that the magnitude of the friction force

exerted by the surface on the spool is given by


              ┌ I + mR1R2  ┐
          f = │──────│T
              └ I + m(R2)^2┘

http://tinyurl.com/ye37j4l


我的疑問：

設摩擦力為f，那麼合力矩 τ= f*R2－T*R1 = I'α

這個轉動慣量I'，我覺得應該要換成I+m(R2)^2才合理

但是我手邊的詳解卻是直接把I'以I(題目所給，也就是轉軸穿過CM的轉動慣量)來代

考慮滾動的時候，轉動慣量不是應該要修正嗎?

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◆ From: 218.172.249.14
※ 編輯: deepwoody       來自: 218.169.100.27       (02/17 23:29)
→ SmArTyau:你修正轉動軸時,力與力臂的關係不需要改嗎?
→ deepwoody:那這個物體是不是就不是"滾動"了呢
推 chieh0206:你f和T都是以轉軸當支點算力矩,所以I也要用中心轉軸
→ deepwoody:謝謝，我懂了