A string is wrapped around the spool and a mass
m
, which is attached to the string, is allowed to fall.
(See next page)
(a) Draw a free body diagram showing the forces on the falling mass,
m
, in terms of
m
,
g
and
F
T
.
(b) If the magnitude of the linear acceleration of the mass,
m
, is measured to be
a
, what is the equa-
tion that should be used the calculate the tension,
F
T
, in the string (i.e., what equations relates
m, g
,
F
T
and
a
)?
Note:
In a system where
F
T
–
mg
=
ma
, if
a
<
<g
then
F
T
≈
mg
.
(c) What is the torque,
τ
, on the spool-axle-disk system as a result of the tension,
F
T
, in the string
acting on the spool?
(d) What is the magnitude of the angular acceleration,
α
, of the rotating system as a function of the
linear acceleration,
a
, of the falling mass and the radius
, r
s
, of the spool?
(e) If the rotational inertia of the axle and the spool are neglected, what is the rotational inertia,
I
, of
the large disk of radius r
d
as a function of the torque on the system,
τ
, and the magnitude of the an-
gular acceleration,
α
?
(f) What is the theoretical value of the rotational inertia,
I
d
, of a disk of mass
M
and radius
r
d
in
terms of
M
d
and
r
d
?
UNIT 12
HOME WORK AFTER SESSION THREE
➡
SmartPhysics:
View the Prelecture 19 “Angular Momentum” before the class of next ses-
sion and answer the checkpoint questions. (The online Homework is due the next day.)
•
Finish Unit 12 Entries in the Activity Guide
(Due before class)