Unit 3 Centripetal Force
Objective
Circular motion is one of the basic motions among the universe. Electrons in an
atom, turning of a car, and revolution of planets all utilize centripetal force. In this
experiment we use an electric motor to rotate an object and demonstrate the relations
between the mass of the object, rotation radius, time period, and the centripetal force.
Apparatus
Centripetal force device (rotation platform, springs, weights, hanger…etc.), optical
timer, optical gates, horizontal level device.
Side post
Springs
Center post
c
Thread
Pulley1
Pulley 1
b
Thread a
Indicator bracket
Balance
Pulley2
Rotating platform
r
Mass
Belt & Motor
Weights
Knob
Fig. 1. Centripetal force device. (Equilibrium without rotating)
Principles
When an object of mass m making circular motion with a constant speed v and the
radius r on a horizontal plane, the centripetal force of this object is
mv 2
F=
= mrω 2 = Mg ………………..(1).
r
(M= mass of the hanger and weights)
v is the speed along tangential direction, and ω is the angular speed (ω=r × v).
Furthermore, v in Eq. (1) can be expressed as
v=
2π r
……………………………………(2)
T
From Eq. (1) and (2), we have the centripetal force as a function of T
4π 2 mr
……………………………..(3).
F=
T2
In this experiment, we vary m, F, and r in Eq. (3) and measure the periods of those
circular motions under different conditions to discus and demonstrate the relations of
centripetal force F with other physical quantities.
Instructions
I. Preparations
1. Adjust the horizontal level of the centripetal force device. Make sure that the
device is horizontal in every direction.
2. Measure the weights of the hanger and all the weights, and put the numbers
down.
3. Put 7 weights on the hanger, and tight 3 threads on the three hooks of the
rotation object. Thread a and b go through pulley 1 and 2 respectively (as
shown in Fig. 1); a is fasten on the hook, and b on the spring. Thread c is
fasten on the top of the side post.
4. Adjust the height of pulley 1 and the position of the side post (16 cm from
the center post), making thread a and b horizontal, and c vertical. The
distance of the side post from the center post is required to set as 16 cm.
5. As shown in Fig. 2, adjust the indicator bracket on the center post making the
upper edge of the indicator disk (orange and circular plate) just pass the
indicator bracket. This is set as an indicator showing that thread a and b are
horizontal.
Q1: What are the physical meanings when the upper edge (surface) of the
indicator disk (orange plate) just passes the indicator bracket except that
thread a and b are horizontal.
Fig. 2.
Fig. 3. (Equilibrium without rotating)
Balanced condtition.
Unbalanced condition.
II. Vary the mass of the object m under static rotation radius r and centripetal
force F
1. Put 7 weights on the hanger, and adjust the position of the post, making
thread c aim at the reference line (vertical line on the post). Record the
position of the side post as the rotation radius r. And the weights on the
hanger provide the centripetal force F.
2. Adjust the indicator bracket on the center post, making the upper edge of the
indicator disk just pass the indicator bracket.
3. Remove the hanger, and install the optical gates to let pulley 1 pass this
optical gate when making rotation (as shown in Fig. 3). Increase the voltage
of the power supply smoothly until the indicator disk return to the initial
position (upper edge of the indicator disk pass the indicator bracket). Select
function 5 of the optical timer.
Q2: What is the centripetal force under such condition?
4. Record the time period of 5 cycles and get the time period T. Repeat 5 times,
and calculate the average value and standard deviation.
5. Unfasten a slice from the object, and measure the new mass m of the object.
Repeat step 2, 3 and 4 for time period T.
6. Unfasten another slice, and measure another new mass m. Repeat step 2, 3,
and 4 for T.
7. Do the plot of m versus T 2.
Q3: If the indicator disk cannot match the indicator bracket steadily but
oscillate through the indicator bracket, what do you think the reasons are?
Can you overcome this problem?
III. Vary the rotation radius r under static F and m
1. Put 7 weights on the hanger. Fasten 3 slices and measure the mass of the
object. Adjust the position of the side post making thread c aim at the
reference line (vertical line) on the side post. Measure the rotation radius
(position of the side post).
2. Adjust the indicator bracket on the center post and make the indicator disk
3.
4.
5.
6.
7.
8.
aim at the indicator bracket (as described previously).
Remove the hanger, and place the optical gate across pulley 1. Then
smoothly increase the voltage to start the rotation until indicator disk is back
to the initial position. Select function 5 of the optical timer.
Record the time period of 5 rounds and get the period of each cycle. Repeat 5
times and get the average value and standard deviation.
Change the rotation radius: reduce 1 cm each time, and be sure to re-adjust
thread a and b to horizontal level, and c to vertical level. The easiest way is
to wind thread b on the hook which it is fastened to reduce its length.
Repeat step 2, 3, and 4 and get the new time period T.
Change the radius again (you are required to get T of 5 different radius).
Do the plot of r versus T2.
IV. Vary centripetal force F under static r and m.
1. Put 7 weights on the hanger, and set the radius as 12 cm. Fasten 3 slices of
the object as the rotation object. Get the average period T and the standard
deviation.
2. Remove a weight from the hanger to change the centripetal force. Re-adjust
threads a, b, and c (to the horizontal and vertical level). Start the rotation and
get the period (in the same way as mentioned previously).
3. Repeat step 2 until 5 weights are removed (you are required to set 5 different
F).
4. Do the plot of F versus T2.
Q4: Can you derive Eq. (3) from II, III, and IV?
Remarks
1. Make sure that the power supply is at C.V. mode and then increase the voltage.
Utilize ‘FINE’ knob for fine tune, and do not over increase the voltage or you may
damage the rotation device. Start the measurement after the rotation is stable.
2. Wipe off the dust of the device and check whether there’s dust on the bearing.
3. The object may shift when you change the centripetal force. Remember to adjust
thread b to make the object back to the required position, or otherwise the rotation
radius r may not be the position of the post.
4. All the quantities are required to be in the form of X ± σ X , and be careful of the
error propagation.