The purpose of this lab is to investigate uniformly circular motion by investigating the forces that lead to circular motion.

## Part A: Circular motion caused by a string

Calculate the number of revolutions per minute N required to keep the hanging mass at an angle of 45 degrees from the vertical as it rotates around.

(HINT: first find v as a function of the quantities in the problem such as R, m, g, q, etc. Next recall that the period of the motion *T *(not to be confused with the tension T in the string) equals the distance travelled divided by the velocity, so *T* = (2pR)/v. This gives you the time in seconds for one revolution, but we want the number of revolutions in one minute: N = 60/*T*.)

N =

Now MEASURE the number of revolutions in one minute for your apparatus if the mass is kept at 45 degrees.

N_{expt} =

Now compare the theoretical and experimental values.

% Difference =

## Part B: Circular Motion with the spring attached

If the spring keeps the hanging mass exactly vertical as it spins around at a known number of revolutions per minute, derive an expression for the spring force F_{s} that is required for this motion. (First draw a freebody diagram for the situation.)

(Answer: F_{s} = 4p^{2}Rm/*T*^{2} )

Measure the time for one revolution by timing 20 revolutions and dividing by 20. Record your mass value and the radius of the circle.

Calculate the theoretical spring force:

F_{s} =

Measure the length of the spring when the mass is vertical.

x =

Use another technique to __measure__ the force required to stretch the spring to that length.

F =

Now compare the theoretical and experimental values.

% Difference =

## Conclusion