This paper discusses lead time constant of yaw angular velocity based on equations of motion of automobiles in planar motion. However, the equations of motion are too complex to be interpreted because the steering angle input generates two variables, lateral and yaw angular accelerations simultaneously. Under reasonable assumption, I derive an equivalent transformation models that generates only one acceleration value from the equations of motion. To generate only one variable against steering input, rigid body of an automobile is replaced by two particles located at the front and rear axles. The equations of motion of the equivalent transformation models imply a mechanism of automobiles transient behavior as follows. Steering angle input causes a yaw angular acceleration around the rear axle. This acceleration changes into a yaw angular velocity by time integration. The yaw angular velocity causes an attitude angular velocity of the rear axle. The velocity changes into an attitude angle at the rear axle by time integration. This attitude angle generates a yaw angular acceleration as restoring yaw moment. In this equivalent transformation models, lead time constant of the yaw angular velocity implies time difference between the yaw angular velocity and attitude angle at the rear axle. Therefore the lead time constant is suitable for criteria of behavior of the automobile at the rear axle. Furthermore the equations of motion will introduce a control law to improve automobile dynamic behaviors.