Uniform Circular Motion
1. Consider a bob of mass m attached to a rotating platform by a string of length l as shown in the
figure. Assume the platform rotates with a frequency f and the string makes an angle  with the
vertical as shown in the figure.
a) Draw a free-body diagram for the mass and explain what force allows the bob to move in a
circle. Next to your diagram indicate the direction of the bob’s acceleration. What is the direction
r
of the net force acting on the bob?
l

m
b) Apply Newton’s Second law to the motion of the bob. In particular write down two equations
that express how the net forces in the horizontal and vertical directions are related to the
accelerations in those respective directions.
b) How is the speed of the bob related to its rotational frequency f and the lengths l and r? How
is the bob’s acceleration related to these quantities?
c) Using the equations you found in parts (b) and (c) determine the rotational frequency f of the
bob that will allow the string to make an angle  = 30 with the vertical.
d) Obtain a rotational device at the front of the room and make the appropriate measurements to
determine the lengths l and r. Using these to predict the period of the bob when it revolves at a
rate that will allow  = 30. Given your limitations on determining l and r estimate the
uncertainty of your prediction.
e) Test your prediction by rotating the device so that  = 30 while measuring the period. To
estimate the period measure the time for N > 1 revolutions and divide by N. Does the choice of N
have any influence on the measurement error of the period? Compare your measured value with
your prediction and comment on whether it is within your experimental uncertainties.
2. Suppose a spring is attached to the bob while it rotates. Assume that the bob rotates at a
frequency f sufficient to allow the cord to hang vertically as shown in the figure.
a) Draw a free-body diagram for the bob. What is the direction of the bob’s acceleration and the
net force acting on the bob?
b) In terms of m, r, l, f, and g, determine the force that the spring exerts on the bob while it is
rotating as shown in the above figure. What force acts on the spring that allows it to be pulled
outward?
c) Rotate the platform so that the bob hangs vertically and measure the frequency of rotation.
From this frequency predict the force that the spring exerts on the bob while it is rotating.
d) Using a spring scale (obtain one that has maximum deflection) stretch the spring to the same
extent it was stretched while it was attached to the rotating bob. What force does the spring exert
when it is stretched by this amount? How does this force compare with the force you found in
part (c)?