# Direct Measurement Video of a Ball Sliding and Rolling

## Summary

This activity is intended to help students understand and apply rotational mechanics. Students will use a video of a billiard ball that is sliding and rolling along a metal track. Students can use the video to determine what coefficient of friction would cause the motion of the ball.

Students will use a QuickTime video recorded at 480 frames per second, making measurements directly from the video using a frame-counter and numerical data overlaid on the video.

The video at right is a preview of the video students use for the activity.

## Learning Goals

Students will:

• engage in open-ended problem solving
• apply rotational mechanics using a realistic video representation of a ball rolling and sliding
• make accurate measurements from a video
• to determine a method to find the coefficient of friction using rotational mechanics and measurements from the video
• calculate the angular acceleration of the ball using measurements from the video and rotational kinematics
• recognize and apply the connection between angular acceleration and torque
• examine how friction causes the torque that is responsible for the rotation of a rolling object
• determine the coefficient of sliding friction that causes the ball to roll
• analyze the results of their work for validity

## Context for Use

This activity is intended for an introductory physics course that includes rotational kinematics and mechanics. Advanced high school courses, including AP Physics C and AP Physics 1, include these topics. It is helpful if students have some experience with direct measurement video analysis before working on this problem. Specifically, students should already know how to:
• use frame-counting, position, and velocity measurements to find the acceleration of objects in a direct measurement video
• use rotational kinematics to calculate the angular acceleration of a rotating object
• calculate the rotational inertia of a rotating object, such as a rotating solid sphere
• apply Newton's Second Law for rotation

This can be a written homework assignment, an in-class activity, or a group assignment. Students will need access to a computer to view and analyze the video.

This is a challenging problem. Students may need coaching to keep them from becoming discouraged. Encourage them to persist. Remind them that the solution is within their grasp. One student's reaction to this activity was: "This problem seemed impossible until someone showed me how to do it. Now it seems obvious." Another students commented that she like this activity because when she found the solution, she felt "smart". Having the problem explained to them will satisfy their curiosity, but prevent them from achieving the satisfaction of figuring it out for themselves.

## Description and Teaching Materials

The simplest and most challenging prompt is to simply ask students to use the video to determine the coefficient of sliding friction between the ball and the track surface. Many students are not accustomed to this type of open-ended problem solving, so the instructor needs to facilitate and coach to encourage students to persist.

Here are three prompts that the instructor can give students:

• Ask them to measure the elapsed time for the ball to rotate pi/2 radians. This may lead them to consider using this interval to calculate the angular acceleration of the ball.
• Ask students to determine the angular velocity immediately after the collision between the pendulum and the ball.
• Ask students what force causes the torque responsible for the angular acceleration of the ball.

The student instructions below include these and other prompts and make this question much easier, because they guide students to the solution. Instructors are encouraged to modify these instructions to suit their students' experience with this type of analysis. Giving fewer prompts may make finding the solution more rewarding and satisfying.

Download the QuickTime file: Video of a sliding and rolling ball (Quicktime Video 5.1MB Apr29 13) here.

Student Instructions:

Ball Sliding and Rolling instructions google doc

Student instructions for sliding and rolling ball (Microsoft Word 2007 (.docx) 662kB Mar24 13)

## Teaching Notes and Tips

Students need a computer with QuickTime video player installed to be able to view the video. Ideally, each student can use a computer 1-to-1. The YouTube version at the top of this page can be controlled using the spacebar on some browsers. Although this is not as easy as using QuickTime, it does work.

The time required to solve this problem varies greatly. Some students will see a path to the solution quickly and complete the activity in as little as 15 minutes. Some students can become frustrated or impatient if they don't see a path to the solution. The instructor's job is to provide encouragement, and as few hints as possible to keep students on task.

If this activity is used in class, the instructor might want to have another activity available for students to work on if they complete this one. That way the class environment stays focused so all students can work to complete this problem.

## Assessment

There are two main goals, and each can be assessed differently. To assess student ability in using videos for open-ended problem solving, use another of the activities in this resource. For example, consider:

Direct Measurement Video: Rotational Inertia of a Bike Wheel

or

Direct Measurement Video: Friction of a block sliding on a Ramp

To assess student mastery of this topic, consider a question from the AP physics exam. Question M3 from the 2012 exam is similar to the one in the video. You can find many AP Physics questions and solutions here