Chapt. 12
Rotational Dynamics
115
13. Dingo the daredevil dog is back—just accept it.
He is now on a noslip track and he curls
himself into an exactly spherically symmetric ball (but not necessarily a uniform density one)
of radius
r
Dingo
. Starting from
REST
, he rolls down the track from an initial height
y
0
. The
track becomes level at
y
= 0, does a circular looptheloop of radius
R
, and then goes level at
y
= 0 again. Note
r
Dingo
and
R
are different radii.
a) What is Dingo’s centerofmass speed at any height
y
assuming he stays on the track?
b) Find a general expression for the normal force on Dingo when he is on the loop as a function
of the angle
θ
between a general radial vector and the radial vector pointing to the top of
the loop and radius
R
.
c) For what
θ
is the normal force expression smallest? What is the normal force expression
for this angle?
d) What is the condition on
y
0
/R
for the normal force
NOT
go less than zero anywhere on
the loop? What happens if it did go less than zero?
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 Fall '06
 Buchler
 Physics, Force, General Expression

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