Unit 8 Circular Motion Notes
2nd Nine-Weeks
Week # 06
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Physics
Unit 08: Circular Motion (Notes)
I. Centripetal acceleration.
1. A merry-go-round 6 m in diameter has the outside edge moving at 3 m/s.
__________________ a. What is the centripetal acceleration? [3 m/s2]
__________________ b. How many g’s is this? [0.306 g’s]
__________________2. A car’s tires enable the car to have a centripetal acceleration of 0.5g. How
fast can it go around a curve of radius 110 m? [23.2 m/s]
__________________3. An airplane goes in a circle at 195 m/s. If the pilot can stand 6 g’s, what is
the smallest radius turn he can make? [647 m]
Unit 8 Circular Motion Notes
II. Centripetal Force
__________________ 4. What centripetal force is necessary to make a 1800 kg car go around a
curve of 22 m radius at 6 m/s? [2945 N]
__________________ 5. Your mass is 80 kg. You make a right turn at 10 m/s around a curve of
radius 18 m. What “centrifugal force” do you feel? [444 N]
III. Critical Velocity
__________________ 6. What is the slowest speed this rollercoaster can have at the top of the
loop that has a diameter of 6 m? [5.42 m/s]
IV. Pendulums/Springs
__________________ 7. What is the period of a grandfather clock with a pendulum 0.4 m long?
[1.27 s]
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Unit 8 Circular Motion Notes
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__________________ 8. What is the period of this mass as it vibrates? m = 3 kg k = 400 N/m
[0.544 s]
V. Circular Motion
_______________________9. Convert 2500 rpm (revolutions per minute) to radians/sec.
_______________________10. Convert 8 rotations into radians.
_______________________11. Convert 175 radians/sec to rpm (revolutions per minute).
_______________________ 12. What is the rotational inertia of a bicycle wheel that is 0.750 kg and
50 cm in diameter?
_______________________ 13. What is the rotational inertia of a softball with a mass of
0.350 kg and 9 cm in diameter?
Unit 8 Circular Motion Notes
14. A car’s tires are 0.60 m in diameter. They spin at 180 rpm. How fast is the car moving?
_______________________ (a) Convert rpm to rad/sec
_______________________ (b) How fast is the car moving?
_______________________ 15. A bicycle is moving at 18 m/s. The tires are 0.70 m in diameter.
How many rpm are the tires spinning?
16. A 5 kg disc has a diameter of 0.30 m. A force of 5 N is applied to the rim for 20 seconds. The
disc starts from rest. What rotational speed (in rpm) does it attain?
_______________________(a) Calculate the inertia of the disc.
_______________________ (b) Calculate acceleration.
_______________________(c) Calculate velocity
_______________________ (d) Convert the velocity from rad/sec to rpm (rev/min)
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Unit 8 Circular Motion Notes
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Circular Motion Formula Page
ac
v2
= -----------r
Fc
vc =
√
rg
rollercoaster
yoyo
satelite
m v2
= -----------r
T
Orbits
Racetracks
1
= -----------f
frequency and period
are reciprocals
T = I α [F x r = I α ]
½ m r2
Iball = (2/5) m r2
Iring = 1 m r2
ω = v/ r
ω is angular velocity, the units are rad/sec
∆x = Vot + ½ a t2
V = Vo + a t
V2 =
Vo2 + 2 a ∆x
1 min = 60 sec
1 revolution = 2 Π or
1 m = 100 cm
V in rad/sec
a in rad/sec2
∆x in rad
6.28 rad
√
l/g
Pendulum
T =2∏
C=2 Π r
Idisc =
T =2∏
√m/k
Spring
1 g = 9.8 m/s2