Teaching physics with Michael Jackson’s Moonwalk: a kinematic exploration for the classroom

Abstract

We present and discuss, from a kinematic point of view, the dance movement known as the Moonwalk, popularized by Michael Jackson over 40 years ago. This paper explores the application of kinematic analysis to enhance physics education by examining the Moonwalk movement. We use the free software Tracker to register the position and time of three material points: the head (H) and the tips of the right and left feet (RF, LF) for two dancers. We found that head movement is well described by a constant speed model and the foot-to-head speed ratio close to the expected value of 2. We also observed an asymmetry in leg movement that impacts the speed of the feet in relation to the dancer’s head. We conclude by discussing possibilities for using dance and other body movements as motivation for physics classes at the high school and university level.

Keywords:
Mechanics; kinematics; video analysis; dance; moonwalk

1. Introduction

Dance is an artistic form of change and movement. We can use physics laws to translate and explain the most beautiful movements into a mathematical language that has its own beauty. Some textbook authors mention dance movements to present physical concepts. To illustrate the motion of the center of mass, it is usually mentioned the ballet movement grand jeté, in which the dancer jumps in the air, raises his arms and stretches his legs horizontally, so that while his head and torso move approximately horizontally (creating the illusion that the dancer floats in the air), the center of mass still describes a parabolic trajectory [¹]. Another commonly cited example involves an ice skater who adjusts her angular speed of rotation by bringing her arms closer to or further away from her body, demonstrating the principle of conservation of angular momentum [¹]. These two examples show that while physics creates models to describe movement based on the resulting forces acting on the body, the dancer seeks to improve his technique by understanding the limitations imposed on his body by nature. Two beautiful discussions of the role of dance as a laboratory for the study of physics can be found in the works of Coates and Demers [²] and Laws [³]. In both books, the authors show that the principles of physics allow us to understand how the human body moves, such as the limitations in a jump due to the force of gravity.

In this work, we present and discuss how the dance movement known as the Moonwalk can be used as a tool for teaching kinematic concepts. Popularized by Michael Jackson on March 25, 1983 (see “Motown 25 – Yesterday, Today, Forever (NBC 1983)” available at https://youtu.be/w_o8EqU3A-E?si=Ts8hBr4LD3wslnt8&t=4860), the Moonwalk creates the illusion of forward walking while the dancer actually moves backward.

The observed effect is that the dancer’s upper body appears to smoothly flow backward, creating an illusion unlike anything seen in traditional walking. When Michael Jackson performed this dance he showed no indication of which foot was supporting his body weight. Through a combination of subtle footwork and upper body movement, he created the illusion of simply floating, revealing his very own style. The Moonwalk movement, despite not having been invented by him, was recorded in art history due to his style, with the help of several choreographers and directors who he held in high esteem and who helped him shape his ideas into a clear movement [⁴]. This innovative dance move has been adapted and performed in various contexts, including underwater by the USA artistic swimming team, who recently won a silver medal at the Paris Olympics [⁵].

Some authors point dancing, or art in general, as a motivating theme to engage students in scientific learning, by grouping educational subjects into science, technology, engineering and mathematics, or simply STEM [⁶]. Following this technological trend, the analysis of the movement of the human body according to the laws of Physics, as exemplified by the Moonwalk, can be interesting because it has applications in biomechanics [⁷, ⁸]. Companies like Boston Dynamics develop robots that imitate the movement of animals aimed at inspection, facilities management, automation, security, research and development applications [⁹].

This paper is organized as follows. In Section 2, we detail the recordings of the Moonwalk that will be analyzed. In Section 3, we use the Tracker [¹⁰] software to perform the video analysis, making kinematics considerations. In Section 4 we make the final considerations.

2. Methodology

To perform the Moonwalk, the dancer must follow these steps (repeatedly – see, for example, [¹¹, ¹²]): 1) bend the right foot in half-point and shift the body’s weight onto it; 2) slide the left foot backward; 3) bend the left foot in half-point and shift the body’s weight onto it; 4) slide the right foot backward. When executed correctly, this motion creates the illusion of forward movement while the dancer is actually moving backward.

Although numerous recordings of MJ performing the Moonwalk exist, most do not meet the criteria for proper video analysis, which requires a fixed camera, the dancer moving perpendicularly to the line of sight, and a clear length reference for position measurements. We were able to find a footage at MJ’s private studio that satisfies these requirements (see “Amazing Clip of Michael Jackson Practicing for a Performance!” Available at https://youtu.be/rc4uWbkCECM?si=TL5ujpElT0h0h1WP)¹. A screenshot of this footage can be seen in Figure 1. Due to the limited resolution of the said video, and to be able to compare the original moonwalk to a non-professional dancer, we produced our own video recording.

Figure 1
Screenshot of Michael Jackson practicing the moonwalk at his studio.

We study the Moonwalk movement using tools and technological resources that are accessible to teachers and most students who are interested in carrying out the activity: a tripod, smartphone and computer. To analyze the motion, we used the free software Tracker [¹⁰], which allows registering the position and time of chosen points of the moving object (for recent examples, see [¹³, ¹⁴, ¹⁵]). This software allows for both manual (frame-by-frame) and automatic tracking of points, provided they are sufficiently distinct from the background. Additionally, Tracker enables the visualization of graphs and the automated calculation of derived physical quantities, such as speed and acceleration, for each material point.

Co-author SDTS performed and filmed the Moonwalk dance using a smartphone at a rate of 120 frames per second in slow-motion mode to provide better quality recording of the experimental points. We chose a well-lit, flat area measuring approximately 4 meters to allow for multiple steps, while minimizing parallax errors. To calibrate the coordinate axes, we converted the film dimensions (pixels) to the real dimensions (meters) using an object of known size in the filming scene. For the SDTS recording, a 50 cm measuring tape was positioned along the movement path. To facilitate the tracking procedure, red pieces of tape were fixed to the dancer’s feet and shoulders, serving as reference points. We used a static camera positioned perpendicularly to the movement surface, mounted on a tripod, to ensure accurate capture of the Moonwalk. To enhance the stability and naturalness of the dance, SDTS began and ended the moonwalk outside the camera’s field of view, avoiding transient intervals (such as starting from rest and stopping). Figure 2 presents a composite image of a portion of the recording. The full video is available in the supplementary files of the journal. In the Michael Jackson footage, we have used the size of his foot – 9.5 inches (see “Michael Jackson’s moonwalk shoes up for auction” available at https://abcnews.go.com/US/michael-jacksons-moonwalk-shoes-auction/story?id=54663374). The MJ clip used has 30 FPS.

Figure 2
Composite image of part of the moonwalk recording performed by co-author SDTS.

We chose three material points to record positions as a function of time: the right foot’s tip, the left foot’s tip, and the head (left ear for the co-author’s video and hat tip for Michael Jackson’s video). Tracker’s automatic registration feature was only used for the SDTS’s ear, which was clear and undistorted throughout the movement of the video. Manual tracking was required for MJ’s hat because of low resolution and for the feet, due to their overlapping during the Moonwalk. After data acquisition, we created data files containing position and time records for each of the three material points, for each video. To calculate speeds from the videos, we employed a numerical derivative of position with respect to time using the following equation:

(1)$${\upsilon }_i\frac{x\left[i+n\right]-x\left[i-n\right]}{t\left[i+n\right]-t\left[i-n\right]},$$

where i is the frame number, x represents the position, t the time and the calculation is performed around n neighboring points. This was done to minimize fluctuations in speed measurements, since small uncertainties in positions increase significantly when calculating their derivatives. Note, therefore, that while we are reducing noise in the speed measurements, we are actually determining the average speed of the feet and head. Alternatively, teachers and students can use the basic graphical and statistical tools available in spreadsheets or those provided directly by Tracker.

3. Results

3.1. SDTS’s moonwalk

This section presents the results of the moonwalker recorded by us. Figure 3 shows the position as a function of time for the three material points studied in the video analysis: (1) left foot (open green squares); (2) right foot (open blue circles); (3) head (filled black circles). In this plot, the markers of the material points parallel to the time axis indicate that the respective foot is at rest. Between t = 0 s and t ∼ 0.6 s, the right foot is at rest while the left foot slides until t ∼ s. After a brief interval with both feet at rest, the feet switch roles, that is, the right foot slides in the interval 0.6 s ≤ t ≤ 0.9 s while the left foot remains at rest between 0.4 s ≤ t 1.0 s. Taking the head’s movement as a reference (filled markers), we can see that the steps of the right foot (while sliding) indicate a relatively greater inclination compared to the steps of the left foot. This suggests an asymmetric motion pattern as the feet stop and slide alternately.

Figure 3
Tracking of feet and ear of SDTS’s moonwalk. Only 1 every 6 data points are shown (except for the inset).

The head’s movement data, as shown in Fig. 3, suggests a uniform motion. Thus, we performed a linear fit, represented by a solid red line, resulting in the following values (x = x₀ + vt):

(2)$$x_0=(0.1028\pm 0.0007)\text{m}$$

and

(3)$$\upsilon =(0.7246\pm 0.0002)\text{m/s}\text{.}$$

The χ² for this fit was χ² showing that the constant speed model is a good representation for the head motion. Although the feet motion initially appears to also be linear, a closer examination (inset in Figure 3) reveals deviations from the straight line, indicating that the motion exhibits variations in velocity, as we will see next.

Figure 4 shows the velocities of SDTS’s feet and head, calculated using equation (1) for n = 10. The horizontal lines represents the speed averages. We first note that the head speed fluctuates only slightly around the average, while the feet speeds show much more pronounced variations. For the head movement, we determined an average speed of ${\overline{v}}_h=(0.72\pm 0.05)$ m/s, in agreement with the value obtained from the curve fit (equation (3)). For the feet, we obtained averages ${\overline{v}}_{LF}=(1.5\pm 0.7)$ m/s (left foot) and ${\overline{v}}_{RF}=(1.7\pm 0.7)$ m/s (right foot). Thus, the average speed for the left foot is marginally lower than that of the right foot. This result supports the observation made in Figure 3 regarding the asymmetrical motion as the feet alternately stop and slide.

Figure 4
Speeds of the feet and ear of SDTS’s moonwalk.

To assess the smoothness of the motion, we computed the dispersion of the speeds relative to the average for SDTS’s performance, and found

(4)$$\frac{{\sigma }_{\upsilon }}{{\overline{\upsilon }}_h}=\frac{0.05}{0.72}\simeq 7\%,$$

where σ_v is the standard deviation of the speeds. This relatively low value suggests that the head’s movement was highly consistent, contributing to the illusion of effortless floating.

3.2. Michael Jackson’s moonwalk

The chosen clip for analysis features Michael Jackson performing the Moonwalk three times in succession (to the camera left, to the right and left again). Since the three have similar characteristics, we will focus on the third one (see “Amazing Clip of Michael Jackson Practicing for a Performance!” available at https://youtu.be/rc4uWbkCECM?si=TL5ujpElT0h0h1WP).

Figure 5 shows the position as a function of time for the same three tracked material points. We observed the same general behavior in the Moonwalk dance movement performed by SDTS. However, for SDTS, the dominant leg during the movement is the right one, whereas the data from Michael Jackson shows that the left foot exhibits a steeper slope than the right foot (when sliding) indicating an asymmetrical movement as the feet alternately stop and slide.

Figure 5
Moonwalker by MJ. The first 10 data points of the head were excluded from the analysis.

The head’s position, represented by filled circles in Fig. 5, suggests that it is described by a uniform motion and, for simplicity, we performed a linear curve fit, finding the following values (x = x₀ + vt):

(5)$$x_0=(-0.056\pm 0.006)\text{m}$$

and

(6)$$\upsilon =(0.866\pm 0.004)\text{m/s,}$$

where x₀ and v are, respectively, the initial position and speed. The value of χ₂ for the best-fit is χ₂ = 0.000283.

The best-fit line is represented by a solid red line in Fig. 5. The first 10 data points of the head were excluded from the analysis, since he was starting his movement from rest.

Figure 6 shows the speeds for MJ’s feet (using a window of n = 4 points) and head (n = 2 points). The markers shape and color correspond to those in Figure 5. The solid red line shows the average head speed, calculated as ${\overline{v}}_h=(0.8\pm 0.1)$ m/s, in accordance with that determined by the best-fit (equation 6).

Figure 6
Moonwalker speeds for MJ obtained by equation (1). Window of n = 2 points for the head and n = 4 for the feet.

The uncertainty obtained from the average head speed is significantly higher than that from the best-fit (equation 6), as well as in the SDTS recording. However, the uncertainty from the best-fit is likely underestimated, as position measurement errors from the Tracker software were neglected in our analysis.

In Table 1 we summarize the results for MJ and SDTS movements. If the dancer takes equal step lengths with both feet, in the same time interval, and a seamless transition from one foot to the other, each foot should travel the same distance as the head but in half the time. This means that we expect the (average) speed of each foot, during movement, to be twice the speed of the head/body, just as in a regular walk [¹⁶]. However, as shown in the last rows of Table 1, we found that this does not occur exactly. For SDTS, the slower left foot moves approximately 2.1 times faster than the head, while the faster right foot moves 2.3 times faster than the head. In contrast, for MJ, the ratio between the faster left foot and the head is close to the expected factor of 2 (2.1), but the ratio for the slower right foot compared to the head is 1.5. In general, SDTS’s feet move more quickly compared to MJ’s feet, but on the other hand, SDTS’s head movement is slower.

Table 1
Summary of results for SDTS and MJ.

Body Part	SDTS	MJ
Head (m/s)	0.7246	0.866
Right foot (m/s)	1.7	1.3
Left foot (m/s)	1.5	1.8
Ratios
Right/Left foot	1.1	0.7
Left/Right foot	0.9	1.4
Fast Foot/Head	2.3	2.1
Slow Foot/Head	2.1	1.5

We also compute, for the head’s movement, the dispersion of speeds relative to the mean. For the MJ motion, we obtain

(7)$$\frac{{\sigma }_{\upsilon }}{{\overline{\upsilon }}_h}=\frac{0.1}{0.8}\simeq 12\%.$$

The observed difference in dispersion between Michael Jackson (12%) and amateur dancer SDTS (7%) was unexpected. While SDTS’s performance exhibited a high degree of consistency, Michael Jackson’s movements were notably more dynamic and expressive. This variability can be attributed to several factors, including the quality of the video recordings, the dancer’s mass, height and shoes, the floor surface, and their particular dance styles, all of which contribute to the complexity of the Moonwalk choreography.

The recordings used in this chapter were made from a single side, so the foot on the opposite side will occasionally be obscured, resulting in some lost frames. Nevertheless, this does not compromise the analysis, as the lost frames represent a small fraction of the total (8% in the SDTS video).

4. Discussion

This paper explores the potential of bridging dance and physics teaching through the video analysis of the Moonwalk. We analyzed two Moonwalk videos, one produced by our team and another by Michael Jackson, focusing on the kinematics of three body parts: the head, left foot, and right foot.

We found that the head motion of both dancers is well described by a constant speed model, providing an excellent opportunity for educators to introduce kinematic concepts starting from the simplest model. This approach allows students to focus on the fundamentals of uniform motion (and linear fits, for undergraduate students) before tackling more complex scenarios. In contrast, the motion of the feet is more intricate (see Fig. 4), involving noticeable variability. This complexity can be leveraged to discuss fundamental concepts such as the average speed: simple theoretical considerations suggest that the feet, while in motion, should travel at an average speed approximately twice that of the head. Our results partially corroborate this expectation (see Table 1), offering a valuable opportunity for critical analysis and discussion of experimental deviations. These aspects highlight the video analysis of the Moonwalk as a rich pedagogical tool, combining accessible visualizations with meaningful physical interpretations.

The primary goal of this work is to demonstrate how the Moonwalk can be used to teach kinematics. Determining the intrinsic properties of the Moonwalk, however, would require analyzing multiple recordings of the same dancer to estimate variations arising from random factors, such as variations in motion or external conditions. This approach lies beyond the educational focus of the present study but could be explored in future research.

There are many opportunities for the physics teacher to work with his class, whether in secondary school or higher education. In dance, the human body is in motion and has constraints not only due to anatomy, but also to the action of the environment on the body that walks, runs, jumps, squats, and slides. The teacher can use the human body as an instrument of analysis for exploring Physics principles [¹⁷]. By analyzing classical dance movements like the grand jeté and fouettés, trendy ones like the slick back [¹⁸], or even playful activities like cartwheels and trampoline jumps, students can gain hands-on experience and apply Physics concepts to real-world scenarios.

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• 1
  This footage appears to have been sourced from the documentary Michael Jackson’s Private Home Movies (see “Michael Jackson shows you his home videos.” Available at https://m.imdb.com/title/tt0417965/?ref_=ext_shr_lnk)

Publication Dates

• Publication in this collection
  17 Feb 2025
• Date of issue
  2025

History

• Received
  05 Sept 2024
• Reviewed
  23 Nov 2024
• Accepted
  10 Jan 2025