Equations of Motion

Normal and Tangential Coordinates

For an object moving along a path which is curved the components of the forces can be shown in the tangential and normal directions.

Tangential direction: ∑ Ft = mat Acts(points) tangent to the path of the object.
Normal direction: ∑ Fn = man Acts(points) toward the center of curvature of the path.
- an is equal to (v^2 / ρ) where ρ is the radius of curvature(distance from center to point on path) and v is the velocity.


Cylindrical (Polar) Coordinates

These coordinates are used when dealing with angular motion and knowing the radial line for the path of the object.

∑ Fr = mar Radial line
∑ Fθ = maθ Angle measured from the radial line


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Force and Acceleration - Dynamics

Newton's second law states that: F=ma
where F is the force that acts on an object, m is the mass of the object, and a is the acceleration of the object.
This equation is commonly known as the equation of motion.

However, some objects may have more than one force acting on it. The resultant force will be the vector summation of the individual forces.

Common forces are: weight, friction, spring, and normal.

A free body diagram is useful for showing the forces on an object.


Rectangular Coordinates
Forces on an object can be expressed in i, j, k components.
∑ Fx = max
∑ Fy = may
∑ Fz = maz


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