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向心加速度的概念,是高中物理教学中的一个重点和难点,难就难在“匀速圆周运动的加速度的方向”,是指向圆心的这一点上。为了突破这一难点,教材用图一所示的Δv方向的办法,是比较直观的。运用矢量平移法则,将B点处速度矢量v_B平移到A点处,在右方得到一个矢量三角形XYZ,加速度a的方向就跟速度的增量Δv的方向相同。教材配合图一加以数学论证,当Δt趋近于零时,Δφ也趋近于零,则α趋近于π/2,从而可见Δv垂直于v_A并指向圆心。
The concept of centripetal acceleration is a key and difficult point in high school physics teaching. It is difficult to “acceleration in a uniform circular motion” in difficulty. It is a point that points to the center of the circle. In order to overcome this difficulty, the teaching method using the Δv direction shown in Figure 1 is relatively intuitive. Using the vector translation method, the velocity vector v_B at point B is translated to point A, and a vector triangle XYZ is obtained at the right side. The direction of the acceleration a is the same as the direction of the increment Δv of the velocity. The teaching materials are mathematically demonstrated in conjunction with Fig. 1. When Δt approaches zero, Δφ also approaches zero, then α approaches π/2, so that Δv is perpendicular to v_A and points to the center of the circle.