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Ph 111.01
October 20, 2008
PS 8a (20)
Problem 1 = WalkerP 1049.
A
1.29
kg hoop with a radius of
9.8
cm rolls without slipping and has a
linear speed of
1.51
m/s.
M
R
v
ω
v
=ω
R
(a) Find the translational kinetic energy.
J
(b) Find the rotational kinetic energy.
J
(c) Find the total kinetic energy of the hoop.
J
Solution.
We are going to want the angular
velocity
ω
:
( )
()
1.51 m/s
15.41 rad/s
0.098 m
v
R
==
=
.
And the moment of inertia:
2
22
1.29 kg
.098 m
0.01239 kgm
IM
R
=
.
(a)
Calculate the translational kinetic energy:
( )( )
2
2
11
1.29 kg
1.51 m/s
1.471 m/s
KM
v
=
translational
(b)
Now the rotational kinetic energy:
( )( )
2
0.01239 kgm
15.41 rad/s
1.471 J
KI
=
rotational
total
translational
rotational
In the case of the hoop, the two kinetic energies are equal!
(c)
So for the total kinetic energy we just add the results from parts (a) and (b):
1.471 J + 1.471 J = 2.942 J
KK
K
=+
=
Problem 2 = Walker P. 1051.
When a pitcher throws a curve ball,
the ball is given a fairly rapid spin. A 0.15 kg baseball with a radius
of 3.7 cm is thrown with a linear speed of
42
m/s and an angular
speed of
36
rad/s. Assume that the ball is a uniform, solid sphere.
(a) Calculate how much of its kinetic energy is translational.
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This note was uploaded on 05/13/2010 for the course PHYSICS 111 taught by Professor Staff during the Fall '08 term at S.F. State.
 Fall '08
 Staff
 Energy, Kinetic Energy

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