Conservation involves momentum and energy.

Momentum

Momentum is the description of an object in motion.  It is always conserved, meaning initial momentum is equal to final momentum. The variable for momentum is P and its units are Kg-m/s.

P_before=P_after

_{Change in momentum is mass times change in velocity.}

_*P=m*v

_{The change in momentum is also equal to the impulse of the force acting on the object.  Impulse is the amount of force exerted during a certain amount of time.}

_*Impulse=F*t

_{Therefore,  m*v=F*t.                         Momentum Sample Problems}

_Energy

_{Energy is always conserved in some form.}

_{Example:
Think of a ball on a ramp. The ball initially has gravitational potential energy (GPE). As the ball rolls down the ramp, it loses GPE and gains kinetic energy (KE).}

_GPE=mgh

_KE=(1/2)mv²

Now think of a mass on a spring. At the places of maximum displacement, the elastic potential energy (EPE) is the greatest.

EPE=(1/2)kx²
 

Collisions

Energy is always conserved in collisions, but not necessarily in the form of KE.

There are two types of collisions, elastic and inelastic.

Elastic collisions conserve momentum and KE. In reality, there is no such thing as a perfectly elastic collision. For perfectly elastic collisions,

P_before=P_after and KE_before=KE_after

Inelastic collisions conserve momentum but do not conserve KE.  In reality, there is no such thing as a perfectly inelastic collision.  The KE that is lost is converted into other energy, such as heat.

Work

Work is energy.  There are many equations for work because energy can be transferred in many ways. In two-dimensional motion, work is the force times the displacement. Because force and displacement are both vectors, they need to be in the same horizontal or vertical direction for work to be done. A more precise equation for work includes the cosine of theta.

W=FD (cosØ)

Work is done in inelastic collisions to change kinetic energy into other forms of energy, as previously stated.

Power is work over time. It is the time rate of doing work.

P=W/t                                                         Sample Work Problems

Circular Motion

Circular motion involves objects traveling in circular paths. As it travels, it has a velocity known as angular velocity.  The angular velocity can be found by the distance it travels in radians divided by time.

w=ø/t

Centripetal motion is center-seeking motion. In reality, there is no such thing as centripetal force, but centripetal force is equal to the net force on an object in circular motion. Forces on an object in centripetal motion can include tension, gravity, friction, and normal. The formula for the centripetal force on a object is the mass of the object times the angular velocity squared, all over the radius.

F_centripetal=F_net=(mv²⁾/R

In centripetal motion, the direction of acceleration is always towards the center. The velocity, however, is tangent to the circle. The acceleration is expressed as the angular veloctiy squared over the radius.

a_centripetal=v²/R                                               Sample Centripetal Problems

Important Equations

Sample Problems

Additional Help-Here are some websites to help understand the idea of Conservation.
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