Angular Motion (8, 4)

Equations:

θ = θ 0 + ω 0 t +

1

⋅ α ⋅ t2

θ = θ 0 + ω ⋅ t +

1

⋅ α ⋅ t2

 

 

 

2

 

 

2

 

θ = θ 0 +

1

⋅ (ω 0 + ω ) ⋅ t

ω = ω 0 + α ⋅ t

 

2

 

 

 

 

 

 

Example:

Given: Θ 0=0_°, ω0=0_r/min, α=1.5_r/min^2, t=30_s.

Solution: Θ =10.7430_°, ω= 0.7500_r/min.

Circular Motion (8, 5)

Equations:

ω

=

v

ar =

v2

ω = 2 ⋅ π ⋅ N

 

 

r

 

r

 

Example:

Given: r=25_in, v=2500_ft/s

Solution: ω=72000_r/min, ar=3000000_ft/s^2, N=11459.1559_rpm.

Terminal Velocity (8, 6)

Equation:

v =

2 m g

Cd ⋅ ρ ⋅ A

Example:

Given: Cd=0.15, ρ=0.025lb/ft^3, A=100000_in^2, m=1250_lb.

Solution: v=1757.4709_ft/s.

Escape Velocity (8, 7)

Equation:

v =

2--------------------- G ⋅ M

 

R

Example:

Given: M=1.5E23_lb, R=5000_mi.

Solution: v=3485.1106_ft/s.

536 Equation Reference

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Image 472
HP 50g Graphing, 48gII Graphing manual Angular Motion 8, Circular Motion 8, Terminal Velocity 8, Escape Velocity 8