Kinetics of Particles: Force and Acceleration

Kinetics of Particles: Force and Acceleration

Kinetics is the branch of dynamics that relates the motion of bodies to the forces that cause them. This chapter focuses on Newton's Second Law.

Newton's Second Law of Motion

Newton's Second Law states that the unbalanced force acting on a particle is proportional to the time rate of change of its linear momentum. For a constant mass, this reduces to:

∑F=ma\sum \mathbf{F} = m \mathbf{a}

Equations of Motion

Rectangular Coordinates: ∑Fx=max\sum F_x = m a_x ∑Fy=may\sum F_y = m a_y

Normal and Tangential Coordinates: ∑Ft=mat\sum F_t = m a_t ∑Fn=man=mv2ρ\sum F_n = m a_n = m \frac{v^2}{\rho}

D'Alembert's Principle

Dynamic problems can be treated as static problems by introducing an "inertial force" vector −ma-m\mathbf{a}. ∑F+(−ma)=0\sum \mathbf{F} + (-m\mathbf{a}) = 0 This vector acts opposite to the direction of acceleration.

Example: Block on an Incline

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