EXPERIMENT 4- Circular Motion
PHYS 1401
OBJECTIVE
The purpose of this experiment is to calculate the centripetal force needed to keep an object in uniform
circular path. We accomplish that in two ways; by finding the weight needed to stretch a rotating mass
until it reaches a sensitive probe and also by allowing this mass to rotate at a speed necessary to make it
reach the same probe.
MATERIALS
Centripetal force apparatus
Slotted weights
Vernier Caliper
Weight hanger
INTRODUCTION
When a particle of mass m moves in a uniform circular motion of radius r, its velocity v changes
direction and the centripetal force Fc needed for the object to stay around this path is directed toward the
center of curvature of the path and has magnitude given by Fc = m r ω2
where ω is the angular velocity of the object in radian/sec. It is measured by
measuring f which is the number of revolutions per second the apparatus
rotates through where ω = 2πf. By substitution we get the theoretical value for
centripetal force:
Fc = 4 π2 f2 m r
(1)
The apparatus, see figure ( 2 ), consists of an electric motor that rotates the
centripetal force apparatus. As the apparatus rotates, the inertia of the mass m moves it away from the
center. At a measured distance from the center of rotation, the mass contacts a pivoted pointer P. When
the pointer is aligned with the small screw I, the system is in equilibrium. Weights of mass M can be
hung from the spring of the removed apparatus to extend the spring to the distance of equilibrium. This
gives us another way to calculate the centripetal force given by:
Fc = (m + M)g
(2)
1
Then the calculated centripetal force can be compared with the force necessary to extend the
spring.
EXPERIMENTAL PROCEDURE
1) Clamp the centripetal force apparatus to the chuck of the rotator. Make sure everything is
tight enough Slowly increase the speed of rotation until the pointer is deflected up to the
index mark. Keep the rotor maintained at this speed at which the pointer is against the
index. Now measure the speed of rotation by simultaneously starting the revolution counter
and timing a counted number of turns. Let the timing be at least 30 sec. Take a total of four
sets of measurements and record them.
2) Remove the centripetal force apparatus and suspend it from a secure support. Determine the
total amount of weight that should be hung from the rotating mass to cause the pointer to be
deflected to the index mark. Make sure to include the mass of the rotating object.
3) Using a vernier caliper, measure the radius of the rotational motion; it is the distance from the point
above the index to the line engraved on the rotating mass.
2
EXPERIMENT 4- Circular Motion
PHYS 1401
REPORT FORM
Name _______________________________
Instructor ___________________________
Date _____________________
Part I: Centripetal force from the rotational motion
Radius of circle
_______
Measurement
1
2
3
4
Time, s
Rotating mass m ________
Number of revolution
Centripetal force from ( 1 ) _____________
Part II : Centripetal force from the total weight
Value of M
___________
Total mass hung from spring __________
Centripetal force from ( 2 ) ____________
Percent difference between
the two values of force
_____________
3
f, rev/s
Average
CALCULATION
1) Compute the number of revolution per second from procedure 1 and record it.
2) Using the average value for f, compute the theoretical value for the centripetal force
from equation ( 1 ) and record it.
3) Compute the value for the centripetal force using equation ( 2 ) and record it.
4) Compute the percent difference between the two values for the centripetal force.
4
EXPERIMENT 4- Circular Motion
Review Questions and Exercises
Name_______________________
Due before lab begins. Answer on a separate sheet of paper.
Date ______________________
1) What is the difference between centrifugal and centripetal force?
2) A ball on a string is swung in a vertical circle. The string happens to break when it is parallel
to the ground and the ball is moving up. What trajectory does the ball follow?
3) If an airplane propeller of radius 5 ft rotates at 2000 rev/min. What is the speed of a
point at the tip of the propeller?
4) The period of rotation of the earth about its axis is 24 h. What should be its new
rotational velocity for an object at the equator to be weightless, meaning the normal force
on it is zero?
5) Correct this statement: “ the racing car rounds the turn at a constant velocity of 50
miles/hr “
5
EXPERIMENT 4- Circular Motion
Post- laboratory Questions and Exercises
Name _____________________
Due after completing lab. Answer in the space provided.
Date ______________________
1) How is the centripetal force on the rotating body affected by doubling the linear velocity
and keeping the radius constant?
2) Explain why the spring stretches while the system is rotating?
3) Calculate the linear velocity of the rotating mass and its period of motion.
4) Discuss the sources of the errors in this experiment?
5) What is your conclusion from this experiment.
6