Chapter 10: Rotation Flashcards
What is the equation for an angular position?
s = r(θ) or θ = s/r
What are the units for theta?
radians or revolutions
What is the circumference of a circle?
2(π)r or (π)d
What is one revolution equal to?
C/r = 2(π)r/r = 2π radians
What is one radian equal to?
360 degrees/2π = 57.3 degrees
What is the difference between functions for translation and rotation?
translation is x(t)
rotation is theta(t)
What is the equation for angular displacement?
Δ(θ) = θ2 - θ1
What is the average angular velocity equivalent to?
ωav
What is the equation for ωav?
Δθ/Δt = (θ2 - θ1)/(t2-t1)
What is the direction counterclockwise?
positive (+)
What is the direction clockwise?
negative (-)
What is the instantaneous angular velocity equivalent to?
ω = lim Δt -> 0 of Δθ/Δt = dθ/dt
What are the units for ωav?
radians/s or revolutions/s
What is the average angular acceleration equivalent to?
Aav
What is the equation for Aav?
delata omega/deltat = (omega2 - omega1)/(t2-t1)
What are the units for Aav?
rad/s^2 or rev/s^2
What is the instantaneous angular acceleration equivalent to?
alpha
What is the equation for alpha?
alpha = lim deltat -> 0 of deltaomega/deltat = domega/dt
What is another equation for omega?
omega = dtheta/dt
What are the three improved physics equations?
omega = omega0 + alphat
theta - theta0 = omega0t + 1/2 alpha t^2
omega^2 = omega0^2 + 2alpha(theta=theta0)
What is the equation and simplified equation for rotational speed?
ds/dt = drtheta/dt
v = ds/dt = rdtheta/dt = romega
v= romega
What is the symbol T equivalent to?
period of revolution
What is the equation for T?
2pir/v = 2pi/w
