Rolling motion, angular momentum vector and cross products
Now, for the physics version of Nascar racing. The entries in this
marathon are: a particle, hoop, cylinder, and sphere. These objects
are to race down an inclined plane. Neglecting friction, mechanical
energy of the earthobject (particle, hoop, cylinder, or sphere)
system is conserved. Our textbook proves the kinetic energy of a
rigid body consists of both translational and rotational kinetic
energy,
K
tot
≡
K
transl
+ K
rot
= ½ m v
2
+ ½ I
ϖ
2
,
where v is the speed of the center of mass of the object and I is the
moment of inertia about the center of mass of the object.
Assuming the objects start from rest a height h above the
horizontal tabletop then
E
i
= mgh
and
E
f
=
½ m v
2
+ ½ I
ϖ
2
, and
E
i
= E
f
along with v=r
ϖ
will decide the value of v at the bottom of
the incline and therefore, the winner. So, which object wins the
race?
Angular momentum and torque: revisited
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 Spring '08
 Chen
 Physics, Angular Momentum, Friction, Momentum

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