Chapter 5-8 Formulas

Question 1

Force Equilibrium equation

Answer 1

F=ma=0

Question 2

Apparent weight

Answer 2

Fy=Ny + Wy; N-W=ma; Wapp= W + MAy

Question 3

Static Friction

Answer 3

fsmax (static friction) = Us x N (normal force)

Question 4

Reynolds Number (relating to drag force)

Answer 4

Inertia Force/viscous Force; pv^2L^2/nLv where “p” is density, and “n” is viscosity

Question 5

Drag Force

Answer 5

1/2CdpAv^2 where Cd is the drag coeffecient, “p” is density, A is cross section area, and “v” is velocity

Question 6

Newton unit

Answer 6

kg m/s^2

Question 7

Newton to pounds

Answer 7

1N= .225lbs; 4.45N = 1lb

Question 8

kg to lbs

Answer 8

1kg= 2.20lb; 1lb= .454kg

Question 9

Centripetal Acceleration

Answer 9

ac=v^2/r

Question 10

Uniform circular motion velocity formula (not angular velocity)

Answer 10

v=2pi r/T; or v=2pi rf

Question 11

Orbital velocity formula (speed of satellite in low orbit)

Answer 11

Vorbit= sq rt (gr) (gravity & radius)

Question 12

Inverse Square Law formula (for two interacting objects)

Answer 12

F1 on 2 = F2 on 1= GM1M2/r^2

Question 13

Find gravity of a planet formula

Answer 13

g=GM/r^2

Question 14

Orbital Period formula

Answer 14

T^2=(4pi^2/GM)r^3

Question 15

Find angle (in radians) of a section of a circle

Answer 15

Angle (theta)= s/r (s is arc length, r is radius)

Question 16

Angular speed formula (in terms of period/frequency)

Answer 16

2pi rad/T or 2pi rad f (frequency = 1/T)

Question 17

Speed and angular speed formula

Answer 17

v= angular speed x radius

Question 18

Tangential & angular acceleration formula

Answer 18

at=angular accel (alpha) x radius

Question 19

Torque formula

Answer 19

torque = rF or rFsin (theta), where theta is the angle from the radial line & the direction of the force applied

Question 20

Gravitational Torque

Answer 20

g-torque= rmg

Question 21

Center of gravity formula

Answer 21

Xcg= X1M1 + X2M2 + …/M1 + M2

Question 22

Moment of inertia

Answer 22

I= (Sigma-sum of) Mi Ri^2 (mass times radius squared)

Question 23

Newton’s 2nd law for rotation- relating to angular accel

Answer 23

angular accel (alpha)= net torque/moment of inertia

Question 24

Rolling motion- top of wheel

Answer 24

2v=2(angular velocity) r

Question 25

Critical angle formula

Answer 25

Critical angle = tan^(-1) (0.5t/h); “t” is track width, and “h” is height of the center of gravity

Question 26

Spring force formula

Answer 26

Fsp= K (delta X); K is the spring constant, X is the end of spring displacement

Question 27

Spring constant formula

Answer 27

K=YA/L; Y is Young’s modulus, A is cross-section area, and L is length

Question 28

Stress to Strain formula

Answer 28

F/A= Y(delta L/L); F/A is stress, other side is strain

F= force, A= cross sectional area of object, Y=young’s modulus, L= length of object

Question 29

Tensile strength formula

Answer 29

tensile strength = Fmax/A (where A= cross sectional area, not acceleration)

Question 30

Apparent weight circular motion

Answer 30

Fapp= n + w = mv^2/r

Question 31

Critical speed formula

Answer 31

Vcritical= sq rt (gr) (this assumes normal force = 0 during circular motion- like when bike going through a loop)

Question 32

Angular velocity or position without time variable

Answer 32

Wf^2= Wi^2 + 2&(delta 0); where W is angular velocity, and & is angular acceleration, 0= angle

Question 33

Constant Angular Acceleration

Answer 33

delta (0) = Wi (delta T) + 1/2&(delta T)^2; (0= angle, W= angular velocity, & = angular accel)

Question 34

Circular speed

Answer 34

v=2pi r f, or 2pi r/T

Question 35

Period of satellite orbit

Answer 35

T=2pi r/Vorbit

Question 36

Gravity formula

Answer 36

GM/r^2

Question 37

Banking curve formula

Answer 37

tan(theta)= v^2/(r x g)

Question 38

Tangential velocity

Answer 38

angular velocity x radius