03. Dynamics

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[accordion title=”1. Newton’s Laws of Motion”]

Newton’s First Law: a body will remain in its state of rest or uniform motion in a straight line unless acted upon by a resultant force.
Newton’s Second Law: the rate of change of momentum of a body is proportional to the resultant force acting on it and the change takes place in the direction of the resultant force.
- $F = \frac{d p}{d t}$ in general
- $F = m a$ when mass is constant.
Newton’s Third Law: if body A exerts a force on body B, then body B exerts an equal and opposite force on body A

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[accordion title=”2. Linear Momentum”]

The linear momentum of a body is defined as the product of its mass and its velocity.
Impulse is the product of the force acting on a body and the time interval during which the force is exerted. It is equal to the change in momentum of the body.
- For constant force, impulse = $Δ p = F Δ t$
- In general, impulse = $Δ p = \int F . d t$

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[accordion title=”3. Collision Problems”]

The principle of conservation of momentum states that the total momentum of a system of colliding objects remains constant provided no resultant external force acts on the system.
Conservation of momentum applies to both elastic and inelastic collisions.
- $m_{1} u_{1} + m_{2} u_{2} = m_{1} v_{1} + m_{2} v_{2}$
Conservation of kinetic energy applies only to elastic collisions.
- $\frac{1}{2} m_{1} u_{1}^{2} + \frac{1}{2} m_{2} u_{2}^{2} = \frac{1}{2} m_{1} v_{1}^{2} + \frac{1}{2} m_{2} v_{2}^{2}$
Relative speed of approach = Relative speed of separation
- $u_{2} - u_{1} = v_{1} - v_{2}$

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