26 Electric and Hybrid Vehicles cg m v g FIGURE 2.3 Center of gravity (cg) of a vehicle. _ F i _ F 1 _r y F i _ _ F 2 _ θ _ v F N x z FIGURE 2.4 Forces on a particle. ω(t) T NET Axis of rotation FIGURE 2.5 Rigid body rotation. v dr dt a d v dt = = and . The power input to the particle for the i th force is P F i i = ⋅ v F = i v cos θ where θ is the angle between F i 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 a number of independent torques acting on a rigid body causing it to rotate about one of its central principal axes of inertia as shown in Figure 2.5. If J (unit: kg-m 2 ) is the polar moment of inertia of the rigid body, then the rotational form of Newton’s second law of motion in the scalar form is ∑ T T i = = NET J α i where ω = angular speed (rads/s) and d ω θ d 2 α = = 2 = angular acceleration (rads/s 2 ). dt dt The power input for the i th torque is P T i i = ω .