Circular Motion

相信閣下正在讀AL physics課程吧。其實課程只講了事實的一半。

如果你take moment about contact point，沒錯，只剩下電單車自身的重量mg帶來力矩。

這點，就要用angular momentum來解釋，AL physics是沒有提及的。

首先車輪向前滾動，從右手握拳定律，其角動量方向為out of paper。從前方看，即向右。


圖片參考：http://i601.photobucket.com/albums/tt95/physicsworld9999/physicsworld03Nov141441.jpg?t=1258180948


要提一提角動量是矢量，所以要用矢量相加。


圖片參考：http://i601.photobucket.com/albums/tt95/physicsworld9999/physicsworld04Nov141441.jpg?t=1258180973


當電單車側了，其重量會帶夾力矩。但這力矩是會帶來角動量的改變，並不會令它翻側(AL課程沒有提這點的)


圖片參考：http://i601.photobucket.com/albums/tt95/physicsworld9999/physicsworld05Nov141441.jpg?t=1258180988


(自己想像一下最後角動量的方向，因在平面上很難畫出3D圖形)，你可見到車輪會不停地改變其轉動方向，因角動量不斷在改變，而車身不會翻側。

但若你是在AL physics課程裏，還是take moment about C.G. (centre of gravity)較好





2009-11-14 18:08:26 補充：
The net moment acting on the object is really zero. As for equilibrium of moment, taking moment about any point results in the same answer.

2009-11-14 18:09:56 補充：
One mistake for physics8801, we are the observer from a INERTIA frame, the 'non-inertia force', or what you called 'centrifugal force' DOES NOT exist when we view it from an inertial frame.

首先,車唔係傾斜以利用摩擦力來提供向心力,傾斜只係為左平衡.
我個人認為physics8801答得比較好,佢由2個角度黎解(因為架車唔係static equlibirium)(同埋當你當自己係架車果陣,你會feel到離心力,actually 我覺得e個解釋都唔係好岩,因為跟本冇離心力e樣野,離心只係一種現像,並唔係一種力)
ilovemadonna2009則用左angular momentum黎講,但angular momentum本身亦唔係一種力,所以都係解釋唔到點解take contact point唔得.
總括黎講,physics8801有一個point所以好過ilovemadonna2009

The explanation on the "change of angular momentum" of the rotating wheel is only to make the bicycle not falling down, irrespective whether it is travelling on a straight road or on turning a corner.

In fact, it is true that when you take the point of contact as the pivot, there is only one moment given by the weight. But don't forget that "moment balance" only applies when a body is in equilibrium, either at rest or moving at constant speed. If the moment is not balanced, there should be an acceleration. This is just similar to the principle that under a "balanced force" , an object would either be at rest or moving in a straight line (Newton's first Law). When under the action of an "unbalnaced force" (net force), the object will be under an acceleration.

The bicycle is turning a corner, it is under a centripetal acceleration, which is NOT in an equilibrium state, hence, the presence of a net moment is not unexpected.

More technically, the bicycle, when turning a corner, is an "non-inertia reference system". In such system, the action of 'inertia force" needs to be taken into consideration. Clearly, the inertia force in this case is the "centrifugal force" that acts horizontally outward at the centre of mass of the bicycler and rider system. This centrifugal force, which itself would give rise to a moment, would balance the moment given out by the weight when moment is taken at the point of point at the road. The bicycle rider therefore could "get balanced".

In case the rider doen't incline inward when turning a corner, but to remain erect. Since the weight (which now acts vertically downward through the point of contact with the road) gives no moment, the centrifugal force would then overturn the bicycle because its moment about the point of contact.