A wooden disk is set on its edge on a table top. A string is wrapped around its outer circumference and a hand is pulling on the string horizontally from the top, so that the disk rolls without slipping on the table. The center of the disk is moving with a velocity of 12.0 cm/s. What is the velocity of the hand? V hand Vcenter

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Chapter10: Fixed-axis Rotation
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A wooden disk is set on its edge on a table top. A string is wrapped around its
outer circumference and a hand is pulling on the string horizontally from the
top, so that the disk rolls without slipping on the table. The center of the disk is
moving with a velocity of 12.0 cm/s. What is the velocity of the hand?
V hand
Vcenter
Transcribed Image Text:A wooden disk is set on its edge on a table top. A string is wrapped around its outer circumference and a hand is pulling on the string horizontally from the top, so that the disk rolls without slipping on the table. The center of the disk is moving with a velocity of 12.0 cm/s. What is the velocity of the hand? V hand Vcenter
FORMULAS
s= r0,
1= lever arm
T = FI, where
v = ro,
Torque: t = F(sin0)r
a = ra
Equilibrium: Στ-0
Non-equilibrium:
Στ= Ια
Moments of Inertia for Various Rigid Objects of uniform composition: Point
mass: I= MR2
Moments of Inertia for Various Rigid Objects of Uniform Composition
Hoop or thin
cylindrical shell
1= MR
Solid sphere
R
Solid cylinder
or disk
Thin spherical
shell
-MR
2
MR
1=-
2
Long, thin rod
with rotation axis
through center
I MI?
Long, thin
rod with
rotation axis
through end
ML?
= r®,
1= lever arm
v = ro,
a = ra
Torque: t = F(sin0)r
T = Fl, where
%3D
Equilibrium: Στ-0
Non-equilibrium:
Στ-Ια
Transcribed Image Text:FORMULAS s= r0, 1= lever arm T = FI, where v = ro, Torque: t = F(sin0)r a = ra Equilibrium: Στ-0 Non-equilibrium: Στ= Ια Moments of Inertia for Various Rigid Objects of uniform composition: Point mass: I= MR2 Moments of Inertia for Various Rigid Objects of Uniform Composition Hoop or thin cylindrical shell 1= MR Solid sphere R Solid cylinder or disk Thin spherical shell -MR 2 MR 1=- 2 Long, thin rod with rotation axis through center I MI? Long, thin rod with rotation axis through end ML? = r®, 1= lever arm v = ro, a = ra Torque: t = F(sin0)r T = Fl, where %3D Equilibrium: Στ-0 Non-equilibrium: Στ-Ια
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