PHY131H1S – Class 18
Today:
• Rotational Motion,
Rotational Energy
• Centre of Mass
• Moment of Inertia
Problem Set 7 on
MasteringPhysics due
Friday at 11:59PM
Little intro Ch.12 vocabulary quiz…
Moment of inertia is
A. the rotational equivalent of mass.
B. the point at which all forces appear to act.
C. the time at which inertia occurs.
D. an alternative term for moment arm.
Rotational Motion
An object rotates about an axis. The change in angle
is the same for any point on the object. Its angular
velocity is
The units of ω are rad/s. If the rotation of the object is
speeding up or slowing down, its angular acceleration
is
The units of α are rad/s2.
Center of Mass
The center of mass is the mass-weighted center of the
object.
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Rotation About the Center of Mass
An unconstrained object
(i.e., one not on an axle or a
pivot) on which there is no
net force rotates about a
point called the center of
mass. The center of mass
remains motionless while
every other point in the
object undergoes circular
motion around it.
Rotational Energy
A rotating rigid body has kinetic energy because all atoms
in the object are in motion. The kinetic energy due to
rotation is called rotational kinetic energy.
Here the quantity I is called the object’s moment of inertia.
The units of moment of inertia are kg m2. An object’s
moment of inertia depends on the axis of rotation.
Example
Important Concepts
A ninja-star with mass = 250 g, moment
of inertia 8.5 x 10-4 kg m2, begins at
rest, and then is thrown. The throw
takes 0.20 s, and after the throw the
star has v = 25 m/s, and spins 15
times per second.
a) What was the angular acceleration
during the throw?
b) What is the final total kinetic energy
of the star?
Note: Total kinetic is Klinear + Krotational
2
Four Ts are made from two identical rods of
equal mass and length. Rank in order, from
largest to smallest, the moments of inertia Ia
to Id for rotation about the dotted line.
1/3 mL2
+
mL2
(a) = 4/3 mL2
1/3 mL2
M(L/2)2
0
+ 1/12
+0
(b) = 1/3 mL2
Updated Conservation of Energy…
mL2
(c) = 1/12 mL2
+ 1/3 mL2
(d) = 7/12 mL2
A. Ia > Id > Ib > Ic
B. Ic = Id > Ia = Ib
C. Ia = Ib > Ic = Id
D. Ia > Ib > Id > Ic
E. Ic > Ib > Id > Ia
Ultimate Soup Can race: Cream of Mush vs. Chicken Broth!!
• Two soup cans begin at the top of an incline, are released
from rest, and allowed to roll without slipping down to the
bottom. Which will win?
• Both cans have about the same mass and moment of
inertia.
• Cream of Mushroom soup is more of a thick paste, so when
this can is rolling down the ramp, the soup rotates along
with the can as one solid object, like a solid cylinder.
• The Chicken Broth is more of a liquid, so the metal can rolls,
while the liquid stays oriented up and down without rotating.
Predict:
A. Cream of Mushroom will win
B. Chicken Broth will win
C. Both will reach the bottom at about the same time.
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