Centripetal Force

What’s the Big Idea‽

Does Newton’s Second Law of Motion (ΣF = ma) stand up in rotational kinematics? Let’s find out! In this lab, we’ll be validating the formula ΣF_C = mv² / r, where ΣF_C is the sum of the forces in the centripetal direction, m is the mass, v is the velocity, and r is the radius.

Procedure

This lab seemed simple enough; the idea was that we would construct a pendulum, then measure its centripetal force and linear velocity at a single instance. This absolutely did not go as planned—it seemed like the force probe and the photogate were never working correctly at the same time. However, after several attempts, we somehow managed to get everything in order.

To begin our final attempt, we gathered a stand with a metal rod and clamps to create the structure that the pendulum would be attached to, then used a force sensor, some string, and a metal ball to construct the pendulum itself. At the base of the pendulum, we attached a photogate to measure the velocity of the ball.

Exactly as so!

We connected the force sensor and the photogate to the Vernier LabQuest, profusely checking them to make sure they worked. We also used a meterstick to measure a radius of 0.5 m. Next, we lifted the ball along a circular path and released it, recording the following data:

Though somewhat unrelated, the data from the force sensor approximates a sine curve as it is uniform circular motion 

Less interestingly, the data from the photogate decreases over time as the pendulum slows down.

Hungry for some closure on this lab? Time to see if Newton’s Second Law works in rotational kinematics in the Takeways!

Takeaways

By taking two corresponding points from out two data sets, we can see if the formula ΣF_C = mv² / r, is true. Let’s do some math to see what happens!

And the calculations reveal...

Aha! There is only a 0.002 N difference between the force measured from the sensor and our calculated force, meaning that indeed, Newton’s Second Law does continue to work in this strange rotational land of mystery. Our data only yields a 2.1% difference, which is fantastic, especially compared to some of our other labs. Today we go home in confidence knowing that the universe isn’t, in fact, broken. What relief.