Introduction to Uniform Circular Motion Lab¶

Welcome to the Uniform Circular Motion Laboratory! In this experiment, we will investigate the forces acting on an object in uniform circular motion and verify the relationships between centripetal force, velocity, and radius.

Uniform circular motion occurs when an object moves in a circle at constant speed. The acceleration that keeps it moving in a circular path is called centripetal acceleration, and it is always directed toward the center of the circle. The force responsible for this acceleration is the centripetal force, given by:

$F = \frac{m v^2}{r}$

or equivalently in terms of angular velocity $\omega$ :

$F = m r \omega^2$

where: - $F$ is the centripetal force, - $m$ is the mass of the object, - $v$ is the linear velocity, - $r$ is the radius of the circular path, - $\omega$ is the angular velocity.

What You Will Learn¶

By the end of this lab, you will be able to:

Understand the concept of centripetal force and its role in circular motion.
Measure the relationship between centripetal force, mass, velocity, and radius.
Use force sensors and photogates to collect and analyze data.
Compare experimental results with theoretical predictions.
Discuss the effects of measurement uncertainties and systematic errors.

Overview of the Experiments¶

This lab consists of two main experiments:

Experiment 1: Centripetal Force vs. Velocity¶

Attach a steel ball to a force sensor and rotate it at a fixed radius.
Measure angular velocity ( $\omega$ ) and linear velocity ( $v$ ) using a dual-beam photogate.
Increase the rotation speed systematically and record the centripetal force.
Plot and analyze force vs. velocity squared to verify theoretical relationships.

Experiment 2: Effect of Radius on Centripetal Force¶

Shorten the string length to decrease the radius of rotation.
Repeat the measurements for centripetal force vs. velocity at this new radius.
Compare results for different radii to confirm theoretical predictions.

Equipment You Will Be Using¶

Force Sensor – Measures the tension in the string providing centripetal force.
Dual-Beam Photogate – Determines velocity by measuring the time between beam crossings.
Rotating System with Motor – Provides a controlled circular motion setup.
Steel Ball and String – The object in motion.
DC Power Supply – Controls the motor speed.
Weighing Scale – Measures the mass of the steel ball.
Meter Stick/Ruler – Measures the radius of rotation.
Capstone Software – Collects and processes data from the sensors.