Patel (pnp223) – homework 24 – Turner – (92160)
1
This printout should have 10 questions.
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001
10.0 points
±eng and Isaac are riding on a merrygo
round. ±eng rides on a horse at the outer
rim oF the circular platForm, twice as Far From
the center oF the circular platForm as Isaac,
who rides on an inner horse.
When the merrygoround is rotating at a
constant angular speed, what is ±eng’s angu
lar speed?
1.
halF oF Isaac’s
2.
impossible to determine
3.
twice Isaac’s
4.
the same as Isaac’s
correct
Explanation:
Angular speed is the same For every point
on the merrygoround.
002
(part 1 oF 2) 10.0 points
Consider the problem oF the solid sphere
rolling down an incline without slipping. The
incline has an angle
θ
, the sphere’s length up
the incline is
ℓ
, and its height is
h
. At the
beginning, the sphere oF mass
M
and radius
R
rests on the very top oF the incline.
M
μ
ℓ
θ
h
What is the acceleration oF the center oF
mass?
The moment oF inertia oF a sphere
with respect to an axis through its
center
is
2
5
M R
2
.
1.
a
=
5
7
g
cos
θ
2.
a
=
2
7
g
sin
θ
3.
a
=
3
7
g
cos
θ
4.
a
=
3
7
g
sin
θ
5.
a
=
5
7
g
sin
θ
correct
6.
a
=
3
5
g
cos
θ
7.
a
=
3
5
g
sin
θ
8.
a
=
2
7
g
cos
θ
Explanation:
Consider the Forces acting on the sphere:
mg
cos
θ
N
f
mg
sin
θ
Using the parallelaxis theorem
I
=
2
5
M R
2
+
M R
2
=
7
5
M R
2
,
and because the sphere rolls without slipping,
α
=
a
R
.
With the origin at the point oF contact
between the sphere and the incline surFace,
s
τ
:
M g R
sin
θ
=
I α
M g R
sin
θ
=
7
5
M R
2
a
R
a
=
5
7
g
sin
θ
.
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 Spring '09
 Turner
 Physics, Angular Momentum, Force, Work, Rotation, patel, lever arm

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