Contents

1 Variables 1.1 Time-related 1.2 Distance-related 1.3 Gravitational 2 Cumulative equations 3 Isolated variable equations 3.1 Time-related 3.1.1 ω 3.1.2 N 3.1.3 T 3.2 Distance-related 3.2.1 r 3.2.2 v 3.2.3 a 3.3 Gravitational 3.3.1 MG

Variables

Time-related

• ω angular velocity
• N rotational speed
• T time (of period)

Distance-related

• r radius
• v velocity (tangential)
• a acceleration
  • <math>a_c<math> centripetal acceleration

Gravitational

• MG product of central or total mass and gravitational constant

Cumulative equations

1. <math>\omega \equiv 2\pi N<math>
2. <math>\omega T \equiv 2\pi<math>
3. <math>N T \equiv 1<math>
4. <math>\omega r \equiv v<math>
5. <math>\omega^2 r \equiv a<math>
6. <math>\omega^2 r^3 = MG<math>
7. <math>\omega v = a<math>
8. <math>\omega MG = v^3<math>
9. <math>\omega^4 MG = a^3<math>
10. <math>T v = 2\pi r<math>
11. <math>T^2 a = 4\pi^2 r<math>
12. <math>T^2 MG = 4\pi^2 r^3<math>
13. <math>T a = 2\pi v<math>
14. <math>T v^3 = 2\pi MG<math>
15. <math>T^4 a^3 = 16\pi^4 MG<math>
16. <math>2\pi N r = v<math>
17. <math>4\pi^2 N^2 a = r<math>
18. <math>4\pi^2 N^2 r^3 = MG<math>
19. <math>2\pi N v = a<math>
20. <math>2\pi N MG = v^3<math>
21. <math>16\pi^4N^4 MG = a^3<math>
22. <math>r a \equiv v^2<math>
23. <math>r v^2 = MG<math>
24. <math>a r^2 \equiv MG<math>
25. <math>v^4 = a MG<math>

Isolated variable equations

Time-related

ω

1. <math>\omega \equiv {2 \pi \over T} \equiv 2 \pi N<math>
2. <math>\omega = {v \over r}<math>
3. <math>\omega = {a \over v}<math>
4. <math>\omega = \sqrt{a \over r}<math>
5. <math>\omega = {v^3 \over MG}<math>
6. <math>\omega = \sqrt{MG \over r^3}<math>
7. <math>\omega = \sqrt[4]{a^3 \over MG}<math>

N

1. <math>N \equiv {\omega \over 2\pi} \equiv {1 \over T}<math>
2. <math>N = {v \over 2\pi r}<math>
3. <math>N = {a \over 2\pi v}<math>
4. <math>N = {\sqrt{r} \over 2\pi\sqrt{a}} \equiv \sqrt{r \over 4\pi^2a}<math>
5. <math>N = {v^3 \over 2\pi MG}<math>
6. <math>N = {\sqrt{MG} \over 2\pi\sqrt{r^3}} \equiv \sqrt{MG \over 4\pi^2r^3}<math>
7. <math>N = {\sqrt[4]{a^3 \over MG} \over 2\pi} \equiv \sqrt[4]{a^3 \over 16\pi^4 MG}<math>

T

1. <math>T \equiv {2\pi \over \omega} \equiv {1 \over N}<math>
2. <math>T = {2\pi r \over v}<math>
3. <math>T = {2\pi v \over a}<math>
4. <math>T = 2\pi\sqrt{r \over a} \equiv \sqrt{4\pi^2 r \over a}<math>
5. <math>T = {2\pi MG \over v^3}<math>
6. <math>T = 2\pi\sqrt{r^3 \over MG} \equiv \sqrt{4\pi^2 r^3 \over MG}<math>
7. <math>T = 2\pi\sqrt[4]{MG \over a^3} \equiv \sqrt[4]{16\pi^4 MG \over a^3}<math>

Distance-related

r

1. <math>r = {v \over \omega} \equiv {v \over 2\pi N} \equiv {T v \over 2\pi}<math>
2. <math>r = {a \over \omega^2} \equiv {a \over 4\pi^2 N^2} \equiv {T^2 a \over 4\pi^2}<math>
3. <math>r = \sqrt[3]{MG \over \omega^2} \equiv \sqrt[3]{MG \over 4\pi^2 N^2} \equiv \sqrt[3]{T^2 MG \over 4\pi^2}<math>
4. <math>r = {v^2 \over a}<math>
5. <math>r = {MG \over v^2}<math>
6. <math>r \equiv \sqrt{MG \over a}<math>

v

1. <math>v = \omega r \equiv 2\pi N r \equiv {2\pi r \over T}<math>
2. <math>v = {a \over \omega} \equiv {a \over 2\pi N} \equiv {T a \over 2\pi}<math>
3. <math>v = \sqrt[3]{\omega MG} \equiv \sqrt[3]{2\pi N MG} \equiv \sqrt[3]{2\pi MG \over T}<math>
4. <math>v = \sqrt{r a}<math>
5. <math>v = \sqrt{MG \over r}<math>
6. <math>v = \sqrt[4]{a MG}<math>

a

1. <math>a = \omega r^2 \equiv {4\pi^2 r \over T^2} \equiv 4\pi^2N^2 r<math>
2. <math>a = \omega v \equiv {2\pi T \over v} \equiv 2\pi N v<math>
3. <math>a = \sqrt[3]{\omega^4 MG} \equiv \sqrt[3]{16\pi^4 MG \over T^4} \equiv \sqrt[3]{16\pi^4N^4 MG}<math>
4. <math>a = {v^2 \over r}<math>
5. <math>a \equiv {MG \over r^2}<math>
6. <math>a = {v^4 \over MG}<math>

Gravitational

MG

1. <math>MG = \omega^2 r^3 \equiv {4\pi^2 r^3 \over T^2} \equiv 4\pi^2N^2 r<math>
2. <math>MG = {v^3 \over \omega} \equiv {T v^3 \over 2\pi} \equiv {v^3 \over 2\pi N}<math>
3. <math>MG = {a^3 \over \omega^4} \equiv {T^4 a^3 \over 16\pi^4} \equiv {a^3 \over 16\pi^4N^4}<math>
4. <math>MG = r v^2<math>
5. <math>MG = r^2 a<math>
6. <math>MG = {v^4 \over a}<math>