Mechanics

Question 1

Projectile motion position

Answer 1

Question 2

Velocity difference

Answer 2

Question 3

Centripital acceleration in uniform circular motion

Answer 3

a = v² / r

Question 4

Rotational kinetic energy

Answer 4

Question 5

Spring potential energy

Answer 5

1/2 kx²

Question 6

Change in potential energy in a conservative field

Answer 6

Question 7

Force of a potential

Answer 7

F = -∇U

Question 8

Work force relationship

Answer 8

Question 9

Angular velocity

Answer 9

v = Rω

Question 10

Angular momentum

Answer 10

L = r x p

= Iω

Question 11

Torque

Answer 11

T = r x F

= dL / dt

Question 12

Coriolis force

Answer 12

Question 13

Centrifugal force

Answer 13

Question 14

Moment of inertia

Answer 14

Question 15

Parallel axis theorem

Answer 15

I = I_CM + Mr²

Question 16

Center of mass

Answer 16

Question 17

Lagrangian

Answer 17

Question 18

Euler-Lagrange equation

Answer 18

Question 19

Conjugate momentum

Answer 19

Question 20

Hamiltonian

Answer 20

Question 21

Hamilton’s equations

Answer 21

Question 22

Orbital Lagrangian

Answer 22

Question 23

Orbital angular momentum

Answer 23

Question 24

Orbital effective potential

Answer 24

Question 25

Reduced mass

Answer 25

Question 26

Hooke’s law

Answer 26

F = ma = -kx

Question 27

Angular frequency

Answer 27

Question 28

Satisfaction of Hooke’s Law

Answer 28

Question 29

Normal modes prescription

Answer 29

Question 30

Hyperbolic orbit

Answer 30

E > 0

Question 31

Parabolic orbit

Answer 31

E = 0

Question 32

Elliptical orbit

Answer 32

E < 0

Question 33

Equation of motion for an oscillator with damping, using b

Answer 33

Question 34

Equation of motion for an oscillator with damping and a driver

Answer 34

Question 35

Pendulum natural frequency

Answer 35

ω² = g / L

Question 36

Natural frequency for extended object of mass m swinging on a massles rod of length R

Answer 36

Question 37

Bernoulli’s principle

Answer 37

Question 38

Underdamped

Answer 38

Question 39

Critically damped

Answer 39

Question 40

Overdamped

Answer 40

Question 41

Serial spring constant

Answer 41

Question 42

Amplitude of a driven undamped oscillator

Answer 42

Question 43

Damping parameter

Answer 43

Question 44

Equation of motion for an oscillator with damping, using β

Answer 44

Question 45

Velocity in polar coordinates

Answer 45

Question 46

Velocity in cylindrical coordinates

Answer 46

Question 47

Velocity in spherical coordinates

Answer 47

Question 48

Buoyant force

Answer 48

F = ρVg

Question 49

Kepler’s third law

Answer 49

T=ka^3/2

where a is the semimajor axis

Question 50

Velocity in a circular orbit

Answer 50