Dancing with Physics: Rotational Motion & its Forces

Everyone has at least once seen a dancer pirouetting several times as they dance in their beautiful tutus, or a figure skater turning super fast in the ice rink as they finish an amazing exhibition! But, how do they do that?, what are the physics behind it? and ... how can we actually experience it ourselves?, how can we teach the physics of rotational motion to students through experience? To answer the first two questions, let's start by defining what we need to make a turn:  

• We need a body, a mass to turn.
• We need an axis of rotation.
• We need a propelling force to start the turn.

• We need to gather together (hug) with all the parts of our body, our axis of rotation.

Let's begin by showing the students a very short video to start reflecting on the movement. You can make use of this video or any other that suits the topic the best for you! 

• Do you know what a force is?

• Can you give me examples of forces that you know?

• Choose an open space to try all the exercises proposed in this lesson. In that space set three imaginary lines parallel to each other, two of them equidistant to the third one, wich will be at the middle (see the figures above to guide yourself). 
• The line in the middle will be the starting line, and the other two lines will be the finishing lines.
• Ask the students to stand up, and form 3 or 4 pairs facing each other. Each student from the formed pairs must be on one side of the starting line. 
• The idea of the game is to use their hands to push against each other trying to be the first to push their classmate to the finishing line. Explain this to the students and have fun!
• Repeat it, two, or three times, allow the students to pair with someone else with a different body constitution to theirs.

• Variation 1: Ask your students to sit down in the floor, and pair again with a classmate. Ask them now to pull each other towards them by holding hands.
• Now, ask them to pair with a different classmate with a different body constitution. Repeat the exercise.
• Variation 2: Ask your students to try the game again while standing, but this time ask them to take off their shoes and socks and try the "push and pull" game. Then ask both of your students to deep both of their feet in flour and try the game again. Now, ask one of the students to clean his/her feet while the other remains with the flour on them, and try the "push and pull" game again.

2. In the second experience, when were you pulled by your classmate? When his/her body constitution (mass) was similar to yours, smaller or bigger? When were you pulled the easiest by your classmate? When your constitution was similar to your classmate's, or when it was smaller? Maybe when it was bigger compared to your classmate's body constitution? 3. In the third experience, how did taking off their shoes and/or using flour affected their results? Who won the game, the classmate with barefeet or the classmate which dipped its feet into the flour? Why do you think this was the case? Does the surface affect the result? How?

• Here is a good moment to make the students reflect on the fact that forces have a magnitude and a direction, in one case, the direction of the force, attracted their classmates towards them, and in the other, the applied force pushed away their classmates from them. You can help them visualize this with the aid of arrows drawn in different colors and in different sizes and use them as a visual representation of the applied forces by the students along the different games.

• Use the example of "pushing and pulling" with bare feet vs flour to reflect on how the materials of the different surfaces against their feet change the magnitude of a new force called friction. Let them know that friction is a force that resists movement when two surfaces slide against each other. When the surfaces are smoother between them, the resistance to movement is smaller, and when the surfaces are rougher, then the resistance to movement is bigger, causing a bigger friction that helps them stand steady in the ground while pushing their classmate against the finishing line, with all the force of their body mass.

For the following activity, start the video of MJ at minute 4:00, and let the students observe the dance movement where Michael Jackson defies gravity. Stop the video for the students to analyse. If there's enough time to play the whole video, enjoy it as it is amazing! Questions and Activities for the Students: 1. How is Michael Jackson doing not to fall down? There might be some answers suggesting he is very strong, take these answers as an opportunity to invite them to experience it by themselves. An activity that could lead the students to understand what MJ needs to oppose to the force that is pulling him down, is asking the students to pair up again in to two parallel lines, one of them is facing the other's back in row no. 1 and the other one in row no. 2. In this activity, trust, and security are quite important, take care that all of the students are attentive to that. After making sure that everyone is ready, count to 3 and ask the students in row no. 2 to let themselves go so their classmates in row no. 1 can catch them. You can use the following pictures to guide yourself. 

Reflections:

• The force which is pulling down Michael Jackson is gravity! 
• Hence a force which can pull him up or backwards is needed to balance and stop him from falling! In which ways can we counteract that force? Can you imagine?
• When you hold your friend upwards in the free fall and stop her/him from falling down, you're also applying a counteractive force to gravity.
• Don't say anything, but Michael Jackson's secret is hidden in his shoes... Sshhh... (You can watch it in the video below).

• Ask your students to spread along the classroom for them to have enough space to do the activity.
• Give them the instructions to open their arms, and at the word "spin", start spinning with their opened arms until you give a new instruction.
• Let your students know that you will use the word "hug" when you want them to collect their arms as much as they can towards their bodies.
• Ask them to try different variations of it; both of their arms hugging their bodies, one arm hugging their body and the other one hanging on their side, both arms extended upwards along their axis of rotation, one arm extended towards the ceiling/sky and the other one hugging them, etc.
• Try this exercise several times.

• For this part of the exercise, you will need to bring some pairs of weights of 1 kg, you can also use alternative materials such as a pair of identical thermos/bottles filled with water or maybe sand. 
• Once distributed the weights among the students, give them the same instructions as in the previous part of the exercise.
• Repeat this part of the exercise as many times as necessary.
• Ask the students to notice what happens when they "hug" themselves at your instruction.

• Once the students repetead enough times to have a feeling of what's happening when they close their arms at your instruction, ask them to try again, but with a variant.
• During their spinning time, and after having hugged themselves, ask the students to open their arms again to the sound of the instruction "open".
• Ask them to notice what happened.

• What did you feel when you were rotating and suddenly closed your arms nearby to your body in the first exercise? Was the spinning faster or slower?
• What was the difference in the feeling when using heavy objects in your hands vs not using them?
• Do you think you are experiencing a stronger rotational force? Why?
• What happened when you opened your arms while spinning during this exercise?

• Did you have a similar experience when bringing your leg towards your body while "kicking the ball" in the third exercise?
• What about your experience when spinning while sitting down, did you feel the change in velocity while bringing your legs towards your body?