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Material Type: Notes; Professor: Losert; Class: INTRO PHYS:MECH&RELATIV; Subject: Physics; University: University of Maryland; Term: Unknown 1989;
Typology: Study notes
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m (^) m
What supports forces in the cell? - the cell’s scaffolding
Membrane
Cell ~ 20 μm Dia
Scaffolding
Scaffolding: •Actin filaments •Intermediate Filaments •Microtubules
Scaffolding of a cultured epithelial cell. Microtubules (green) actin (red) (Nucleus is Blue) Image by Steve Rogers.
Moment of Inertia of a Uniform Thin Hoop
For a thin hoop, all mass elements are the same distance from the center
2 2
2
I r dm R dm
I MR
= =
=
∫ ∫
Moment of Inertia of a Uniform Solid Cylinder
( )
( )
2 2
4 2 2 2
ρ π
ρ π ρ π
R z (^) o
z
Total Energy – ball rolling down hill
mechanical energy occurs because the contact point is at rest relative to the surface at any instant
Kf + U (^) f = Ki + U (^) i
U (^) f = Ki = 0 (^1 2 ) 2 2
K (^) f = ICM ω + MvCM
Connecting rotation and COM motion
center of mass:
The acceleration of
the center of mass is
CM
ds d v R R dt dt
CM a dv^ CM^ R d R dt dt
A solid disk and a ring roll down an incline. The
ring is slower than the disk if
1. mring = m (^) disk , 2. rring = _rdisk
rring = rdisk
slower regardless of the relative values of m and r.
A solid disk and a ring roll down an incline. The ring is slower than the disk if
1. mring = m (^) disk , 2. rring = _rdisk
rdisk
slower regardless of the relative values of m and r.
What is the moment of inertia of the following object? R
h
I = MR = πρ R h R = πρ hR
