HP 48gII Graphing, 50g Graphing manual Angular Mechanics 4, Centripetal Force 4, Hooke’s Law 4

Angular Mechanics (4, 2)

Equations:

τ = I ⋅ α	Ki =	1 ⋅ I ⋅ω i2	Kf = 1 ⋅ I ⋅ ω f2	W = r ⋅ Θ
		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	ω	=	v	ar =	v2	ω = 2 ⋅ π ⋅ N
						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 523