Circular Motion Experiment: Velocity^2 vs. Radius Analysis

[smashingtime]

Homework Statement

Hi, I conducted a circular motion experiment--with a rubber bung & string through a plastic tube. I changed the radius of the string every trial, calculated the amount of time for one revolution, and from that derived velocity and velocity^2.

With my data, I graphed Velocity^2 against Radius. I found a linear line of best fit for the graph.
From here, how should I proceed to obtain the formula acceleration = V^2/r?

Thanks!

 

[natugnaro]

a=v^2/r => v^2=a*r

so you need slope of your fit line

 

[Moetasim]

Hello, thank you for sharing your circular motion experiment and data with me. It seems like you have already made some good progress in your analysis by graphing Velocity^2 against Radius and finding a linear line of best fit. This is a great start in understanding the relationship between velocity and radius in circular motion.

To obtain the formula for acceleration = V^2/r, you can use the equation for centripetal acceleration, which is a = V^2/r. This equation relates the velocity and radius to the centripetal acceleration, which is the acceleration towards the center of the circle in circular motion.

To confirm that your data supports this equation, you can compare your calculated values for acceleration using the formula a = V^2/r to the actual accelerations you measured during your experiment. If they are close, then your data supports the equation and you can confidently use it in your analysis.

Additionally, you can also look into the concept of angular velocity, which is the rate of change of angular displacement in circular motion. This is related to linear velocity and can help you further understand the relationship between velocity and radius in circular motion.

Overall, it seems like you have a good understanding of your experiment and its results. Keep exploring and analyzing your data, and don't hesitate to consult with your instructor or other resources for further guidance. Good luck!