Mixed Coordinate System's MAE 202

Speed Rate is?

the tangential component of acceleration in N-T

Acceleration in N-T?

a= v²/p (u_n)+ v^*(u_t)

What equations are still valid if the speed rate is constant?

Constant acceleration formulae

v= v₀ +at

s= s₀+v₀t+1/2 at²

v²=v₀²+2a(dS)

The position formula in constant acceleration will give WHAT in circular motion?

arc length travelled= dS

Radians traveled= ?

arc length/ radius

radians* ____= degrees

180/pi

Rho formula for cartesian to N-T (radius of curvature)

(1+(dy/dx)²)^3/2

——————-

|d²y/dx²|

remember that the dy/dx is with respect to time, so when doing excel formula u need vx³ on bottom cause one factor is from chain rule

U_n always points in which direction?

toward the concavity

U_theta always points in which direction?

in the same direction theta is measured from

dy/dx in the radius of curvature formula can also be found from what values?

V_y/V_x, the velocities at these points

d²y/ dx² is what when vy/vx is dy/dx

v_xa_y - v_ya_x / vx³

one of those vx factors is for the chain rule and deriving w respect to time

Speed Rate in Cartesian

x^*x^**+y^*y^** /sqrt( x^*2+y^*2)

How many Megameters in a Gigameter?

1000

velocity formula in polar?

v=( r^*u_r) + (r theta^*u_theta)

acceleration formula in polar?

(r^**+ rtheta^*2) u_r + (2r^*theta^*+ rtheta^*) u_theta