Angular Mechanics (4, 2)

Equations:

τ = I ⋅ α

1

⋅ I ⋅ω i

2

1

⋅ I ⋅ ω f

2

W = r ⋅ Θ

Ki = --

 

Kf = --

 

 

2

 

 

2

 

 

 

W = Kf – Ki

P =τ ⋅ ω

Pavg

W

 

ω f = ω i +α ⋅ t

= -----

 

 

 

 

 

 

t

 

 

at = α ⋅ r

ω = 2 ⋅ π ⋅ N

ω i = 2 ⋅ π ⋅ Ni

ω f = 2 ⋅ π ⋅ Nf

Example:

Given: I=1750_lb∗in^2, Θ =360_°, r=3.5_in, α=10.5_r/min^2, ωi=0_r / s.

Solution: r=1.1017E–3_ft_∗lbf, Ki=0_ft∗lbf, W=6.9221E–3_ft∗lbf, Kf=6.9221E–3_ft∗lbf,

at=8.5069E–4_ft/s^2, Ni=0_rpm, ωf=11.4868_r/min, t=1.0940_min, Nf=1.8282_rpm, Pavg=1.9174E–7_hp.

Centripetal Force (4, 3)

Equations:

F = m ⋅ ω

2

⋅ r

v

v2

ω = 2 ⋅ π ⋅ N

 

ω = --

ar = ----

 

 

 

r

r

 

Example:

Given: m=1_kg, r=5_cm, N=2000_Hz.

Solution: ω=12566.3706_r/s, ar=7895683.5209_m/s, F=7895683.5209_N, v=628.3185_m/s.

Hooke’s Law (4, 4)

The force is that exerted by the spring.

Equations:

F = –k ⋅ x

W =

–1

⋅ k ⋅ x

2

-----

 

 

 

2

 

 

Example:

Given: k=1725_lbf/in, x=125_in.

Solution: F=-2156.25_lbf, W=-112.3047_ft∗lbf.

Equation Reference 5-23