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1.在粗糙的固定平面上做无滑滚动 半径为R的圆形刚体在粗糙的固定平面上做无滑滚动时,若质心的速度和加速度分别为vc和ac,绕质心转动的角速度和角加速度分别为ω和ac,则有vc=ωR,ac=acR.由此约束条件和质心运动定理、绕质心的转动定理就可以解决相关问题. 例1 如图1所示,半径为R的乒乓球绕质心轴的转动惯量为J=2/3mR2,m为乒乓球的质量.乒乓球以一定的初始条件在粗糙的水平面上运动,开始时球的质心速度为vc0,初角速度为ω0,两者的方向如图1所示.已知乒乓球与
1. In a rough fixed plane, a circular rigid body with radius R is made to slide without sliding. When the sliding is performed on a rough fixed plane, if the velocity and acceleration of the center of mass are vc and ac respectively, the angular velocity and angle of rotation around the center of mass Accelerations are ω and ac, respectively, and vc=ωR and ac=acR. The constraints, the center of mass theorem, and the rotation theorem around the centroid can solve the problem. Example 1 As shown in Figure 1, a ping pong with radius R The moment of inertia of the ball around the mass axis is J=2/3mR2, where m is the mass of the ping pong ball. Table tennis moves with a certain initial condition on a rough horizontal surface. At the beginning, the mass center velocity of the ball is vc0 and the initial angular velocity is ω0. The direction of the player is shown in Figure 1. Known table tennis and