Rotations and Oscillations Test

Equations NOT on the Equations Sheet and some stuff u should probably remember!

ϑ in terms of x and R

ϑ = x/R

ω in terms of v and R

ω = v/R

ω also equal to…

2pi/T or 2pif

α in terms of a and R

α = a/R

v_max in terms of ω and A

v_max = (ω)A

a_max in terms of ω and A

a_max = (ω)²A

(U_sp)_max in terms of k and A

(U_sp)_max = (1/2)kA²

A on a spring

= x_Max

A on a spring (expressed in radians)

= ϑ_Max

x(t) =

Acos(ωt)

v(t) =

-Aωsin(ωt)

a(t) =

-Aω²cos(ωt)

𝚫ϑ =

(1/2)(ω_i + ω_f)t

K_rot =

(L²)/(2I)

Work in terms of torque and delta theta

W = τ ∙ 𝚫ϑ

displacement

𝚫x = (1/2)(v_i + v_f)t

K_trans (in terms of momentum and mass) ₌

(p²)/(2m)

Alternate form of Power

P = Fvcosϑ

Power is = W/change in time and W is =

F𝚫xcosϑ

Angular Momentum of a point particle (use when an object is going to eventually collide with a rotating object)

L = rpsinϑ = mva (where “a” is the distance of closest approach of the particle to the rotation point)

Moment of inertia of a system of particles

I = Initial Sum of m_ir_i²

W_{Net, Ext} =

𝚫E

If no external forces are doing work

E_i = E_f

I_hoop =

mr²

I_disk =

(1/2)mr²

T is given in…

seconds per cycle (s)

v_max =

2pifA or (2piA)/T

a_max =

(2pif)²A or ((2pi)/T)²A

6 things to mention when describing the effect of something (oscillation) (mention AT LEAST 4, underlined you MUST mention)

• max velocity

• period

• potential energy

• kinetic energy

• amplitude

• acceleration

velocity (oscillation) is greatest @…

equilibrium, because no force is displacing it to be at equilibrium thus there is also no acceleration here

When Force is greatest (in oscillations)…

there is zero velocity

delta torq =

change in momentum/change in time

Torque Units

N times meters

Inertia units

kg times m²

Angular Momentum Units

kg times m²/s