Chapter 11 - Rolling, angular momentum & its conservation
What direction does Acom point down a ramp? What is it given by?
Down the ramp in x direction Acomx = gsinθ/1+(Icom/MR^2)
What are concepts of the yo-yo?
Downward Acom = upward Acom Slowed by tension force/torque rolls on axle with r = yoyo's
What is the angular momentum of a rigid body?
L = Iω
What is the angular momentum of a gyro? Torque?
L = Iωr τ = Mgd (or r)
What is the angular moment of a system?
Lsys = ℓ1 + ℓ2 + etc τnet(external) = dL/dt
What is angular momentum?
Particle with mass with linear momentum passes through point A in xy plane, crossing r and p gives us ℓ
What is rolling defined as?
Rolling is a mix of pure rotation and pure translation - Rotation: all points have ω and all points on edge have Vcom - Translation: all points move with Vcom
For a yo=yo, what is the Acom?
Same as defined before
What is Ffs given by on a ramp?
fs = m(acomx + gsinθ)
What is the KE of rolling?
rotational KE + translational KE KE = 1/2(Icom)(ω^2) + 1/2(M)(Vcom^2)
What is the rate of precession of a gyroscope?
Ω = Mgr/Iω
How can you apply newton's 2nd law to angular momentum?
Fnet = dP/dt (linear) τnet = dL/dt (angular)
What is the conservation of angular momentum?
If no net external torque acts on system, L is conserved, dL/dt = 0, ΔL = 0 so Lf = Li and (Iω)f = (Iω)i
During smooth rolling, what happens to Emec?
It is conserved, so Ef = Ei
How do you find the direction of precession of a gyro?
Put hand on disk, curl finger toward rot, and boom (I think)
What is the Vcom of a rolling object? Acom?
Vcom = ωr Acom = αr
During rolling, what is the relationship between Vtop and Vcom?
Vtop = 2Vcom
What are angular momentum equations? Magnitude? (all vectors)
ℓ= r x p ℓ= m(r x v) ℓ = rmvsinΦ
What is true of Acom and Ffs?
They point in the same direction Ffs is rotational, keeps wheel connected to ground
T/F If there isn't any sliding, static friction is present and it is smooth rolling
True
