Circular motion, torque, energy, and work

Circular uniform motion

Ac=V²/r

Fc=mv²/r or F=m(ac)

ac is proportional to r because v=w*r

Velocity perpindicular to centripetal force vector

Torque

t=rFsin(theta)

As r decreases F goes up: Smaller radius closer to pivot, bigger force needed

Static equilibrium

No movement

Often do not know the force at pivot point so torques=0

Clockwise torques=cc torques

Work

W=Fdcos(theta)

How much a force contributes to displacement

0<theta<90 Acting in x direction W is positive

theta=90 no force in same direction as d so W=0 because not helping d move

Bigger than 90 up to equal to 180 away from direction want to go taking away from direction d so W is negative

Work done be kinetic, centripetal, normal force

Kinetic: negative opposite of velocity

Centripetal: zero because always perpin. to motion

Normal: Usually zero perp. to motion but not if moving up and down

Work done by gravity

Wg=mgh

Gravity is a conservative force only depends on height

Power

P=W/t

depends on time now. So smaller time means more power

Also P=FV for constant force parallel to constant velocity

Kinetic energy

KE=1/2mv²

Total work W=deltaKE

Potential energy

Wgrav=-deltaPEgrav

deltaPEgrav=mgdeltaH

Systems

KE and PE convert into one another transforming but delta E=0

Spontaneous change/action always INCREASE in KE

Work can transfer energy into/out of a system

W done BY system Etotal is negative

W done ON system Etotal is positive

Conservation of energy equation

KEi+PEi=KEf+PEf

DeltaKE+deltaPE=0

Non conservative forces conservation of energy equation

KEi+PEi+Wnc=KEf+PEf

Wnc could be friction or tension for example

Inclined planes

Flipped so X component is mgsin(theta) and y is mgcos(theta)

Mechanical advantage

Fresistance or load/Feffort

Pullies provide multiples of force so MA of 4 is nice

Efficiency of energy

Woutput/Winput x 100%

Area under the curve

Calculate area under curve when the two variables are y and x

W=Fd

and F on y axis and d on x axis