module 4 circular motion and applications of newton's laws

uniform circular motion characterized by

constant velocity - centripetal acceleration towards the centre

what type of force is centripetal

resultant; caused by other forces, don’t draw on its own

when friction is towards centre and wheels are not skidding, what type of friction do we use

static

F_s, towards centre =

mv²/r = μ_smg

frictionless banked curved ideal design speed

tanθ = v²/rg

friction banked curve y and x equalities (frictionless is same without friction components)

y: mg + μ_snsinθ = ncosθ

x: nsinθ + µ_sncosθ = mv²/r

conical pendulum y and x equalities

y: Tcosθ = mg

x: Tsinθ = mv²/r

velocity of conical pendulum

v = gLsinθtanθ ( L is length of string)

tension in cord for nonuniform circular motion

T = mgcosθ + mv²/r

motion in accelerated (non-inertial) frames)

Newton’s laws don’t work, so there are bogus forces like centrifugal and Coriolis forces

coriolis force observed

rotation of hurricanes, ocean currents, deviation of a long range projectile to the right in Northern Hemisphere (north to south)

R→ and v→ are 

antiparallel

sum of forces in free fall =

mg→ - 1/2DpAv²(v→/|v→|)

D = drag coefficient

p = density of medium (kg/m³)

A = cross sectional area to airflow

v² = speed²

V_terminal =

√2mg/DpA

when felix baumgartner free fell, his terminal velocity

increased, reached peak, then decreased as the density of the air increased

projectile motion with drag

shorter max height, shorter range, and right side of parabola appears shorter/steeper