The objective of this lab is to investigate the relationship between the radius of a circular path and the time period of an object moving in uniform circular motion.
When an object moves in a circle at constant speed, it experiences centripetal acceleration directed towards the center of the circle. The formula for centripetal acceleration (
\( a_c \)) is given by:
\[ a_c = \frac{v^2}{r} \]
Where:
Radius (m) | Time for 10 Revolutions (s) | Time Period (s) | Speed (m/s) | Centripetal Acceleration (m/s²) |
---|---|---|---|---|
0.5 | 15.0 | 1.5 | 2.094 | 8.78 |
1.0 | 20.0 | 2.0 | 3.143 | 4.95 |
1.5 | 25.0 | 2.5 | 3.768 | 2.97 |
From the data collected, it can be observed that as the radius increases, the time period of the motion also increases. This indicates an inverse relationship between centripetal acceleration and radius, supporting the theoretical framework of circular motion.
The experiment successfully demonstrated the principles of circular motion. The results corroborate the theory that centripetal acceleration decreases as the radius of the circular path increases, while the time period increases. Further studies could explore varying the mass of the object to examine its effect on circular motion.