KEY

Circular Motion Part II
1.
An Indy car with a speed of 120 km/h goes around a level, circular track with a radius of
1.00 km. What is the centripetal acceleration of the car?
(1.11m/s
2
)
2.
Find the centripetal acceleration for each of the following:
(a) a point on the earth’s equator (ignore its orbital motion)(radius of Earth = 6.38 E6 m);
(b) the earth in its orbit around the sun (radius = 1.49E11
m);
(c) the sun’s orbit around the center of the Milky Way (period = 2E8 years; radius =
3E20 m)
a
c
4
2
r
T
2
4
2
(
3
10
20
)
2
10
8
yrs
3
.
15
10
7
sec
1
yr
2
2
.
98
10
10
m
/
s
2
3.
A doughnut shaped space station has an outer rim of radius of 1 km. With what period
should it rotate
for a person at the rim to experience an acceleration of g/5?
(Remember: g = 9.8 m/s
2
)
4.
A stone moves in a circle of radius 60 cm and has a centripetal acceleration of 90 m/s
2
.
How long des it take to
make 8 revolutions?
5.
A car approaches a level, circular curve with a radius of 45.0 m. When the concrete
pavement is dry the coefficient of friction is 1.20. What is the maximum speed at which
the car
can negotiate the curve at a constant speed?
(23.0 m/s)
6.
A laboratory centrifuge operates at a rotational speed of 12,000 rpm (rev/min).
a)
What is the magnitude of the centripetal acceleration of a red blood cell at a
radian dista
nce of 8.00 cm from the centrifuge’s axis of rotation?
(1.27E5m/s
2
)
b)
How does the acceleration compare with g?
(13,000g)
7.
A 1.0 m cord is used to suspend a 0.50 kg tetherba
ll from the top of the pole. After
being hit several times, the ball goes around the pole in uniform circular motion with a
tangential speed of 1.1 m/s at an angle of 20
o
relative to the pole.
a)
The force that supplies the centripetal acceleration is (1) th
e weight, or (2) a
component of the tension force in the string, or (3) the total tension in the string.
Pick one and explain why.
Answer: (2) The centripetal force is pointed toward the center of the circular motion.
In this case, that is the pole. The
only force that is pointing toward the pole at all is a
little bit of the tension force in the string.
b)
What is the magnitude of the centripetal force?
(1.8 N)
8.
A student is to swing a bucket of
water in a vertical circle without spilling any.
a)
Explain how/why this task is possible.
Answer: At the top, the inertia of the water in the bucket makes the water want
to go horizontally instead of straight down. The water crashes into the side of
the bu
cket, pushing the bucket. The bucket is attached to the string, so the
tension in the string helps to pull the bucket around in a circle. However, at the
top, there is no tension in the string. At the top, the weight of the bucket (and
water) provides th
e centripetal force causing the bucket (and water) to move in a
circle.
b)
If the distance from this shoulder to the center of mass of the bucket (ie. radius of
the circle) is 1.0 m, what is the minimum speed required to keep the water from
coming out of th
e bucket at the top of the swing?
(3.1 m/s)
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