Equations

Question 1

Time to fall if Vo = 0

Answer 1

t=(2h/g)^1/2

Question 2

Calculus Definition of Velocity

Answer 2

V=dx/dt

Question 3

Calc definition of angular velocity

Answer 3

ω=dθ/dt

Question 4

Calc definition of acceleration

Answer 4

a= dv/dt 
a= d2x/dt2

Question 5

Definition of angular acceleration

Answer 5

α = dω/dt
α = d2θ/dt2

Question 6

Calc relationship between a conservative force and its associated potential energy

Answer 6

F = -du/dx

Question 7

Equation for weight or gravitational force

Answer 7

W= mg= Fg

Question 8

Modify equation for impulse for when force is constant

Answer 8

Jconstant = FΔt

Question 9

Modify work equation for a constant force and get rid of the dot product

Answer 9

W constant force = FΔrcosθ

Question 10

Modify power equation into non Calc form

Answer 10

P= work/time

P=ΔE/Δt

Question 11

Modify second power equation. To get rid of dot product

Answer 11

P= Fvcosθ

Question 12

Modify torque equation to get rid of cross product

Answer 12

t= rFsinθ

Question 13

Hoop moment of inertia

Answer 13

MR^2

Question 14

Cylinder or disk moment of inertia

Answer 14

1/2 mR^2

Question 15

Thin rod through center of mass moment of inertia

Answer 15

1/12 mL^2

Question 16

Thin rod about one end moment of inertia

Answer 16

1/3 mL^2

Question 17

Parallel axis theorem

Answer 17

= Icm + md^2

Question 18

Relationship between a and α if no slipping

Answer 18

a= rα

Question 19

Modify angular momentum for a point mass into a more useful form

Answer 19

L= rmvsinθ

Question 20

Angular momentum for extended object

Answer 20

L = Iw

Question 21

Equation for physical pendulum

Answer 21

Tpp= 2π(I/mgXcm)^1/2

Question 22

2 equations for speed of satellite in circular orbit

Answer 22

V= 2πr/T
V= (Gm/r)^1/2

Question 23

Equation for g in terms of mass and radius of planet

Answer 23

g= Gm/R^2

Question 24

Escape velocity

Answer 24

(2Gm/R)^1/2

Question 25

Equation of spring SHM

Answer 25

-constants x

Constants= w^2

Question 26

Equation for rotational pendulum SHM

Answer 26

-constants θ

Constant And= w^2

Question 27

Kepler’s second law

Answer 27

T^2 proportional to r^3

Question 28

Newton’s version of kepler’s second law for satellite in circular orbit

Answer 28

Mv^2/r= GmM/R^2

4π^2r^2/r = GmM/r^2

Question 29

Equation of Motion for Constant Velocity

Answer 29

Δx=vt