Download Amusement Park Ride Project

Rotation, Torque, Circular Motion and
Universal Gravity Review Sheet
1.
A car starts from rest and its
wheels constantly accelerate to an
angular velocity of 2 rad/s after two
revolutions. What is the angular
acceleration of the wheel?
2.
A top spins and slows down at an
angular acceleration of -1.5 rad/s2
until it topples. If the top will topple
at an angular speed of 150 rad/s or
less, and the top toppled after
spinning for 45 seconds, what was
the initial angular velocity of the
top?
3.
A bullet fired from the muzzle of
a rifle initially rotates with an
angular velocity of 2200 rad/s. If
the bullet is slowed by friction and
rotates through 480 revolutions
during its 1.4 seconds of flight,
what is the angular acceleration of
the bullet?
4.
A bicyclist is coasting downhill
and puts on the brakes. He has to
stop in 1.5 seconds to avoid a
suddenly stopped car. If his wheel is
rotating at an angular velocity of 20
rad/s, how many revolutions does
his wheel make before he comes to
a stop?
5.
A boat starts with its propeller at
rest. The driver guns the motor,
accelerating the propeller to spin at
a rate of 200 rpm. If it takes 50
revolutions of the motor to rev up to
this velocity, what is the angular
acceleration of the propeller?
6.
A 0.5 kg ball moves in a circle
that is 0.4 m in radius at a speed of
4.0 m/s. Calculate its centripetal
acceleration. (40 m/s2)
7.
Calculate the centripetal force on
the ball in question #6. (20 N)
10. A phonograph record 30.0 cm in
diameter rotates 33.5 times per
minute.
(A) What is the linear speed of a
point on its rim? (0.527 m/s)
8.
A toy cart at the end of a string
0.70 m long moves in a circle on a
table. The cart has a mass of 2.0 kg
and the string has a breaking
strength of 40. N. Calculate the
maximum speed the cart can attain
without breaking the string. (3.74
m/s)
The minute hand of a large clock
is 0.50 m long.
(A) Calculate its linear speed at its tip
in meters per second. (0.000873
m/s)
(B) What is the centripetal
acceleration of a point on its rim?
(1.85 m/s2)
9.
(B) Calculate the centripetal
acceleration of the tip of the hand.
(1.52 x 10-6 m/s2)
11. What is the minimum radius at
which an airplane flying at 300 m/s
can make a U-turn if its centripetal
acceleration is NOT to exceed 4 gs?
(2250 m)
12. A string 1.0 m long breaks when
its tension is 100 N. What is the
greatest speed at which it can be
used to whirl a 1.0 kg stone?
(Neglect the gravitational pull of the
earth on the stone.) (10 m/s)
15. A road has a round hump 12.0 m
in radius. What is the minimum
speed at which a car can leave the
road at the top of the hump? (11
m/s)
13. What is the centripetal force
needed to keep a 3.0 kg mass
moving in a circle of radius 0.50 m
at a speed of 8.0 m/s? (380 N)
16. A physics student swings a pail
of water in a vertical circle 1.0 m in
radius at a constant speed. If the
water is NOT to spill on him/her:
(A) calculate the minimum speed
of the pail of water
14. A 2000 kg car is rounding a
curve of radius 200 m on a level
road. The maximum frictional force
the road can exert on the tires of the
car is 4000 N. What is the highest
speed at which the car can round the
curve? (20 m/s)
(B) calculate the maximum time
per revolution (period) of the swing
17. A 1.0 m string with a 5 g stopper
on the end is whirled in a vertical
circle. The speed of the stopper is 8
m/s at the top of the circle.
(A) What is the speed of the
stopper at the bottom of the circle?
(HINT: Use energy conservation
principles!) (10.2 m/s)
18. What is the angular acceleration
experienced by a uniform solid disc
of mass 2 kg and radius 0.1 m when
a net torque of 10 N·m is applied?
Assume the disc spins about its
center.
(B) What is the tension in the string
when the stopper is at the top of the
circle? (0.27 N)
19. A Round-A-Bout on a playground
with a moment of inertia of 100
kg·m2 starts at rest and is
accelerated by a force of 150N at a
radius of 1m from its center. If this
force is applied at an angle of 90°
from the line of action for a time of
0.5 seconds, what is the final
rotational velocity of the Round-ABout?
(C) What is the tension in the string
when the stopper is at the bottom of
the circle?
(0.57 N)
20. What is the Inverse Squared Law?