15.3 : 旋转运动学方程

For the rigid body rotating with constant angular acceleration, similar to linear kinematics, kinematics equations for rotational motion can be established.

Considering point A on the rigid body executing circular motion, the translational velocity can be formulated by determining the time derivatives of the displacement equation.

Here, the translational velocity is continually tangential to the circular path. It can be represented using the vector product of angular velocity and the position vector. The expression r_Asinθ corresponds to the radius of the circular path followed by point A.

Equally, the linear acceleration of point A can be described as the sum of the normal and tangential acceleration components.

The tangential component gives the time rate of change of magnitude of the velocity, whereas the normal component gives the time rate of change of direction of the velocity.

The acceleration can be expressed in the vector form by taking the time derivative of the vector equation of the translational velocity.  

Here, the first term gives tangential acceleration, whereas the second term gives a normal component of acceleration.