1
Lecture 22
Torque
ACT: Spheres
Two spheres have the same radius and equal masses. One is
made of solid aluminum and the other is a hollow shell of
gold.
Which one has the biggest moment of inertia about an axis
through its center?
A. Solid Al
B. Hollow Au
C. Both the same
Hollow
gold
Solid
aluminum
Mass is
further away
from the axis
2
tan
F
r
mr
α
=
An intuitive approach to torque
A particle of mass
m
is constrained by a massless rod of length
r
to
move in circles about point P. A force
F
is applied on the particle.This
is the only force applied on it. What is the angular acceleration of the
system?
r
F
m
F
r
F
tan
F
tan
produces a tangential acceleration:
tan
tan
F
ma
=
I
t
a
r
α
=
tan
F
m r
α
=
I
τ
α
=
P
Torque
tan
F
r
τ
=
Directions: Both
and
point out
of the screen.
α
G
r
F
×
G
G
τ
α
=
z
z
I
r
F
τ
=
×
G
G
G
θ
sin
Fr
r
F
θ
=
=
×
G
G
Newton’s second law for rotations
r
F
τ
=
×
G
G
G
For each force on a system,
the torque depends on the
point on which it is applied
τ
τ
α
=
=
∑
net,
i,
all forces
z
z
z
I
The angular acceleration will
be the result of adding all
these torques:
τ
≠
G
G
net
Note: In general,
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 Fall '06
 Johnson
 Physics, Force, Inertia, Mass, mg sin

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