Rotational Motion & Astrophysics: Angular Motion

Question 1

What are the parallels between angular and linear motion?

Answer 1

Linear and angular motion are said to be analogous, therefore are very similar to each other.

We can use our derivatives in similar vein, that being:

ω = dθ/dt (v = ds/dt)

α = dω/dt (a = dv/dt)

We can also use our equations of motion in similar vein:

ω = ω₀ + αt (v = u + at)

θ = ω₀t + 1/2 αt² (s = ut + 1/2 at²)

ω² = ω₀² + 2αt² (v² = u² + 2as)

Question 2

What is the formula for calculating angular velocity from revolutions per minute (rpm)?

Answer 2

ω = 2π*revolutions/60

Question 3

What is the formula for calculating angular velocity from frequency?

Answer 3

ω = 2πf

Question 4

What are our basic formulas for the calculation of arc length, velocity, and acceleration in reference to angular motion?

Answer 4

s = rθ

v = rω

aₜ = ra

Question 5

What are our two formulae for radial acceleration?

Answer 5

aᵣ = v²/r

aᵣ = rω²

Question 6

What are our two formulae for centripetal force?

Answer 6

F = mv²/r

F = mrω²

Question 7

How do we find the minimum speed for an object to move in a circular path?

Answer 7

At the critical point where an object just moves in a circular path, tension will be zero.

T = mv²/r - mg

0 = mv²/r - mg

mg = mv²/r (add mg to both sides)

g = v²/r

v² = gr

v = √gr

Question 8

What is the formula for torque?

Answer 8

T = Fr

Question 9

How do we find the component of torque?

Answer 9

sine rule