1. Central Forces – LO3
T. Ferns – 2/7/06 LO’s 1.2.7, 1.2.8

2. Experiment – Central Force and Angular Velocity
Aim
To show the relationship between central force and angular velocity.

3. Theory
In this experiment, the turntable rotates. There must therefore be a centripetal force. This centripetal force will be provided by the hanging mass.
Satellite mass
Hanging mass

4. Theory Therefore: Fc = msrω2 Fc = Wh = mhg mhg = msrω2 As ω = 2π T
4π2 T2
g, ms, r and π are all constant. Therefore:
mh α 1 T2
Confirming this relationship will prove the relationship between central force and angular velocity.

5. Fc = Centripetal Force
g = Acceleration due to gravity
mh = Hanging Mass
ms = Satellite Mass
ω = Angular Velocity
r = Radius of satellite mass’ rotation
T = Period of rotation
Wh = Weight of hanging mass

6. Apparatus
Gear
Griffin Air Bearing
Satellite mass
Hanging mass

7. Satellite Mass
Pulley
Voltmeter
Gear/Motor Assembly
Air Blower
Stopwatch
Hanging Mass

8. Method
The apparatus was set up as shown, with a 10g mass hung from the pulley.
The motor, voltmeter and air blower were all switched on. With the satellite mass at its minimum radius, the gear was set to move the turntable.
The voltage was slowly increased, causing the turntable to rotate more quickly. When the hanging mass moved slightly upwards, the timer was started and the time for 10 rotations was recorded.

9. Method
This process was repeated a further five times.
The mass was then increased in 10g steps, with the process being repeated six times for each mass.
A graph of hanging mass, mh, against 1 was drawn. T2

10. Results Time for ten rotations Mass (kg) t1 (s) t2 t3 t4 t5 t6 tMEAN T

11. Uncertainties
A table of uncertainties should be completed as shown on the next slide.
A full set of example calculations (both absolute and percentage) must also be given but only for one set of results (e.g. for 10g).
Note – the mass is subject to a manufacturer’s calibration uncertainty of ± 1%.

12. Uncertainties Mass (kg) ±1% Random Unc. t (s) % Random Unc. tMEAN (%)
Calib. Unc.
tMEAN (s)
% Calib. Unc.
Reading Unc.
% Reading Unc.
Combined Unc.
T (%)
1/T2
(%)
Absolute Unc.
(s-2)

13. Graph
A graph of hanging mass, mh, against 1 should be plotted.
Error bars should be included, using the values from the uncertainties table. T2

14. Conclusion
The graph of mass against 1/T2 is a straight line passing (almost) through the origin. This confirms the relationship between centripetal force and angular velocity.

15. Evaluation Why does the graph not pass through the origin?
Is the radius constant or was it changing slightly? How could this be overcome?
There may be friction in the pulley system meaning all of the weight was not necessarily converted to centripetal force.
Anything else?