PHYS 1501Q Chapter Notes - Chapter 12, 13: Cross Product, Angular Acceleration, Angular Displacement
19 Dec 2017
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Department
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Professor
12 Rotational Kinematics And Moment Of Inertia
Angular kinematics
●Analogous to linear kinematics
●Angular displacement - θ
●Angular velocity - ω = dt
dθ
●Angular acceleration - α = dt
dω
●For constant angular acceleration
○tαtθ = θ0+ ω0=2
12
○tω = ω0+ α
○α(θ )ω2− ω2
0= 2 − θ0
Relating Linear and Rotational parameters
●Counterclockwise θ 0Δ >
●Arc length s = R θ
●Tangential speed v = R ω
●Tangential acceleration a = R α
Kinetic Energy in Rotations
● = Ksystem Iω
2
12
Moment of Inertia
●Moment of inertia - rI = ∑
mii
2
Moment of Inertia of a Solid Object
●Linear Mass Density: λ = L
M
●= = =m xIz=∫
2
L
−2
L
d2m xλ∫
2
L
−2
L
d2[ ]λ 3
x32
L
−2
LL MLλ1
12
3=1
12
2
●= = =m xIz=∫
L
0
d2m xλ∫
L
0
d2[ ]λ 3
x3
0
LL MLλ3
13=3
12
Moment of Inertia of a Solid Cylinder
● where and are measured relative to a common axis of rotationItotal = ∑
i
IiItotal Ii
●Volume Mass Density: =⍴M
VCylinder
●m r z ϕdr (L)(2π)[ ] (L)(2π) M RIz=∫
d2=⍴∫
L
0
d∫
2π
0
d∫
R
0
r3=⍴4
r4
0
R=M
πR L
24
R4=2
12
Solid Cylinder of Mass (M)
●Moment of inertia about the Axis of Symmetry
○MRIz=2
12
○(M)R IIT op =2
12
12=2
1
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PHYS 1501Q Full Course Notes
Verified Note
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Document Summary
Angular velocity - = dt d . Linear mass density: = l r. 2 are measured relative to a common axis of rotation r3 dr (l)(2 )[ r4. Moment of inertia about the axis of symmetry. Ii are measured relative to a common axis of. Relates moments of inertia about parallel axis. Only movement about the center of mass is rotation. Idumbbell = irod + ileft sphere + iright sphere. Ways to close a door more quickly large . Apply the push perpendicular to the door a nearly parallel pussh will not move large door closes quickly large door closes quickly large r the door. Right hand rule (for determining the direction of: curl fingers in the direction of rotation, thumb points along the direction of . Determining the direction for points in the same direction as points in the opposite direction as. Rotational form of newton"s 2nd law -
