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Learning Introductory Physics with Activities

Paul J. Emigh, Rebecka Tumblin, Kathryn Hadley, Danielle Skinner

Section 11.13 Challenge - Rotational Motion

Explanation 11.13.1. The Bowl.

Shown below is a motion diagram of a ball rolling along a semicircular track. The time intervals between each pair of consecutive points are equal. The ball starts from rest at point 1, and just reaches point 9 before rolling back down the right side of the track.
A motion diagram of a ball on a semicircular track.
Figure 11.13.1.
Complete this motion diagram by sketching qualitatively accurate vectors representing both (a) the instantaneous velocity and (b) the instantaneous acceleration of the ball at each instant.
Your explanation should describe how you used the diagram to determine each vector and detail why the magnitudes of the vectors are the same or different.

A*R*C*S 11.13.2. The Conical Bowl.

You are riding a \(150 \mathrm{~kg}\) bicycle at constant speed along a circular track of radius \(25 \mathrm{~m}\text{.}\) The shape of the track is a conical bowl, so the track makes a consistent angle of 15° with the horizontal. Determine the speed of the bicycle.
Tip 1.
Analyze and Represent: Sketch and label a free-body diagram for the bicycle. Think carefully about what coordinate system you want to choose and break each force into components.
Tip 2.
Calculate: When you are beginning your calculation (part 2a), explicitly identify the concepts, laws, and definitions that are relevant. For example, if you are solving for the magnitude of an object’s angular acceleration, you might decide to use the definition of angular acceleration, \(\alpha = \frac{d\omega}{dt}\text{.}\) Also, remember that your answer and work should be primarily symbolic: you should only plug in numbers at the very end!
Tip 3.
Sensemake: As part of your symbolic sensemaking (part 3c), try a special case using the angle of the track.

Activity 11.13.3. Metacognitive Reflection.

Choose one of the major models or equations that you made use of during this unit on rotational motion. Identify the corresponding model or equation that you have used previously when studying translational motion. Write a few sentences comparing and contrasting the rotational and translational versions.
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