## 22 Laws Of Motion

Newton's second law of motion can be expressed in equation form as follows: where is the net force, m is the effective mass, and a is the acceleration. The law is applied to the vehicle by considering a number of obj ects located at several points of contact of the vehicle with the outside world on which the individual forces act. Examples of such points of contact are the front and rear wheels touching the roadway surface and vehicle, the frontal area that meets the force from air resistance, etc. We will simplify the problem by merging all of these points of contact into one location at the center of gravity (cg) of the EV and HEV, which is justified, because the extent of the object is immaterial. For all of the force calculations to follow, we will consider the vehicle to be a particle mass located at the cg of the vehicle. The cg can be considered to be within the vehicle, as shown in Figure 2.3.

Particle motion is described by particle velocity and acceleration characteristics. For the position vector for the particle mass on which several forces are working, as shown in Figure 2.4, the velocity v and acceleration a are

FIGURE 2.3 Center of gravity (cg) of a vehicle.

FIGURE 2.5 Rigid body rotation.

The power input to the particle for the ith force is where is the angle between Fi and the resultant velocity v.

For a rigid body rotating about a fixed axis, the equivalent terms relating motion and power are torque, angular velocity, and angular acceleration. Let there be i independent torques acting on a rigid body, causing it to rotate about an axis of rotation, as shown in Figure 2.5. If J (unit: kg-m2) is the polar moment of inertia of the rigid body, then the rotational form of Newton's second law of motion is where

The power input for the ith torque is Pi=Ti .

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