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向心加速度是匀速圆周运动中的教学难点,这是由于学生因长期接受标量运算而产生的思维定势,认为匀速圆周运动中物体运动速率不变,故其△v=0,于是有a=△v/△t=0。因此我们在教学中必须强调两点,一是速度的矢量性,速度的方向变化也表示速度有变化,故△v≠0,另一是速度变化的方向就是加速度的方向。因此在教学中必须说清楚△v的方向。教材中引进了速度三角形的方法,实际上已经考虑到了上述两点。关于向心加速度公式的推导方法甚多,下面提供几种有别于课本的推导方法,供大家参考。
Centripetal acceleration is a difficult teaching point in uniform circular motion. This is due to the long-term scalar calculations the students have fixed their mindset. They think that the velocity of the object in the uniform circular motion is constant, so its Δv=0, so there is a= Δv/Δt=0. Therefore, we must emphasize two points in teaching: one is the vectoriality of speed, and the change of direction of speed also means that there is a change in speed, so Δv≠0, and the other is that the direction of speed change is the direction of acceleration. Therefore, the direction of Δv must be clearly stated in teaching. The method of introducing speed triangles in the textbooks has actually taken into consideration the above two points. There are many derivation methods for the centripetal acceleration formula. The following provides several derivation methods that are different from the textbook for your reference.