Centripetal Force and Speed
The purpose of this lab is to investigate the relationship between
the speed of an object in uniform circular motion (UCM) and the
centripetal force on the object.
centripetal force apparatus
washers or weights
data & analysis sheet
A force which pulls an object toward the center of a circle is
called a centripetal force. How much centripetal force needs
to be exerted to cause an object to move in a circle? Your experience
should tell you that the amount of centripetal force that you need to
exert depends on
- the mass of the object you are whirling - heavier
objects require more force,
- how fast you are whirling it - going faster requires more
- the radius of the circle.
The textbook says:
but how can we verify the quantitative relationship between
centripetal force and mass, speed, and radius? This question can't be
answered all at once, since a scientific experiment is designed to
vary one quantity (holding all others constant) and measure its
effect on one other quantity. The most difficult quantity (of
mass, speed, and radius) to hold constant from trial to trial in an
experiment is the speed of the object, so it is easiest to study the
effect of speed on centripetal force, since it is relatively easy to
hold the mass of the object and the radius of the circle
You will use an apparatus similar to the one pictured above to
measure the effect of speed on centripetal force. You can hold the
mass constant during a set of trials by always whirling the same
object. You can keep the radius of the circle constant (with a little
practice) by keeping the upper clip a fixed distance below the glass
tube while whirling the object.
- Place a small number of weights or washers (be sure that all
of the washers you use are the same size.) on the bottom clip of
the apparatus. This part of the apparatus hangs straight down, and
the weight of the washers supplies the centripetal force.
- Practice whirling the stopper (or ball) until you can keep the
top clip a short distance below the bottom of the glass tube while
the stopper whirls. IMPORTANT! If the clip touches the bottom
of the glass tube, the weights are no longer supplying the
centripetal force! If the clip rises or falls appreciably as
the stopper whirls, the radius of the circle is changing.
- Use a stopwatch to measure the time taken for a reasonable
number of revolutions (20 - 30 perhaps). Record your data.
- Change the number of washers on the bottom clip (centripetal
force) and repeat steps 3 and 4. Repeat for several different
weights. Record the data.
- Change the position of the top clip to change the radius of
the circle. Repeat the experiment for this radius. Be sure to
indicate where the radius changes in your data table.
- If you have time, you might try to determine the relationship
between mass and centripetal force. In order to do this, you need
to keep both the radius of the circle and the speed constant while
you vary the mass and the centripetal force. You can design your
own data table for this. You could also investigate the
relationship between the radius and the centripetal force.
- Calculate the period of revolution, T (the time to go around
once) for each trial. Show a sample calculation.
- Calculate the linear speed, v, of the stopper for each trial.
Include a sample calculation. (Note: )
- Theoretically, the centripetal force should be directly proportional to the square of the speed. To check this, add a column to your data table for v2. Construct a graph of centripetal force versus v2. Remember that it is customary to put the
quantity you change (force, in this case) on the horizontal axis,
and the quantity that changes by itself (speed) on the vertical
axis. Be sure that you pick the largest convenient scale for your
graph and draw the best smooth curve through your
Is the graph of centripetal force versus speed squared a straight
line? So, what can you say about the relationship between centripetal
force and speed, then?
last update January 24, 2007 by JL