查看完整版本 : 旋轉慣性+碰撞問題

seahouse 2013-4-29 12:13 AM

旋轉慣性+碰撞問題

[img]http://i1123.photobucket.com/albums/l546/seahouse2/asd_zpsb04b1b1b.png[/img]
A uniform rod, having length L = 0.5 m and mass M = 1 kg, can rotate about anaxis through one end, as shown in the figure. When the rod swings through itslowest position, it collides with a small ball, having mass m =0.1, that sticks to the end of the rod. If the rod’s angularspeed just before collision is 2.4 rad/s, what is the angular speed of therod–ball system immediately after collision? Given that the rotational inertiaof the rod through its centre of mass is (1/12)ML2. please help me

飛天五 2013-5-11 12:11 AM

搵左 I 先...
1/12 ml^2 係 centre of mass o者係Ixx...
但因為佢郁o個點係o係個頭, 所以 I 應該用parallel axis theorem :  i + md^2 加返個 l/2 上去...即係平時書俾o個個 Ix'x'...
= 1/3 ml^2 = 1/3 * 1 * (0.5)^2 = 0.25/3
同個ball 相撞後, 因為有新 mass 加左上去, 所以新o既moment of inertia I = Io + mr^2.... Io = 0.25/3, m=0.1, r=0.5
Inew = 0.25/3 + (0.1)(0.5)^2 = 0.11kg.m^2

By Conservation of Angular Momentum
Io . omegao = I. omega
0.25/3 * 2.4 = 0.11 * omgea
omega = 1.82 rad/s#

[[i] 本帖最後由 飛天五 於 2013-5-11 12:27 AM 編輯 [/i]]
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查看完整版本: 旋轉慣性+碰撞問題