Hammer throw

This activity allows students to understand the transformation of circular motion into linear motion. It develops the ability to analyze a sporting performance with scientific tools.

The hammer throw is one of the oldest Olympic events, with roots in Celtic competitions dating back over 2000 years. In this spectacular discipline, the athlete spins a 7.26 kg metal ball attached to a 1.22-meter steel wire and handle, building rotational speed through three to four turns before releasing it at precisely the right moment. The physics is beautifully clear: during the spinning phase, the hammer follows circular motion, with the athlete providing the centripetal force through the cable. At the moment of release, the hammer transitions instantaneously from circular to linear motion, becoming a projectile whose speed equals the tangential velocity at the point of release. The world record of over 86 meters requires a release speed of approximately 29 m/s at an optimal angle near 44 degrees. Using FizziQ's kinematic analysis module, students can analyze a video of a hammer throw to measure the actual ejection speed and compare it with the theoretical prediction from the rotation rate and cable length.

Learning objectives:

The student analyzes a hammer throw video using the FizziQ kinematic analysis module to determine the ejection speed. After having carried out the pointing image by image the student compares this experimental value with a theoretical value calculated from the rotation speed then thinks about the optimal ejection angle to maximize the distance.

Level:

High school

FizziQ

Author:

Duration (minutes) :

40

What students will do :

- Analyze a hammer throw video using kinematic tracking to determine the release speed
- Compare the measured ejection speed with the theoretical value calculated from angular velocity and rotation radius
- Understand the relationship between circular motion parameters and the resulting linear velocity
- Investigate the optimal release angle for maximum throwing distance
- Apply the concepts of centripetal acceleration, tangential velocity, and projectile motion to a real athletic performance

Scientific concepts:

- Uniform circular movement
- Conservation of angular momentum
- Ballistic
- Rotary/linear motion conversion
- Optimal shooting angle

Sensors:

- Camera (video recording for kinematic analysis)
- FizziQ Kinematics module (frame-by-frame position tracking)

What is required:

- Smartphone or tablet with the FizziQ application
- Hammer throw video available in Cinematic Video Library
- FizziQ experience notebook

Experimental procedure:

Open FizziQ and navigate to the Kinematics module. Load the hammer throw video from the FizziQ video library.
Identify a reference scale in the video. The throwing circle diameter (2.135 m) or the athlete's height can be used.
Set the scale and coordinate origin in FizziQ. Place the origin at the center of the throwing circle.
Track the position of the hammer head frame by frame during the last revolution before release and during the initial projectile phase after release.
During the circular phase, collect at least 10-15 points around the final turn to accurately determine the rotation speed.
Continue tracking the hammer for 5-10 frames after release to determine the initial projectile trajectory.
From the circular phase data, calculate the angular velocity ω by measuring the angle swept per unit time.
Calculate the rotation radius r (distance from the athlete's axis of rotation to the hammer head, typically 1.8-2.2 m including arm length).
Compute the theoretical tangential velocity: v = ω × r.
From the post-release tracking data, determine the actual ejection speed by measuring the distance traveled per unit time in the first few frames.
Compare the theoretical and measured ejection speeds. They should be approximately equal.
Estimate the release angle from the trajectory direction at the moment of release and calculate the theoretical throwing distance using the projectile equation: D = v² × sin(2θ) / g.

Expected results:

For a competitive hammer throw, the angular velocity during the final turn is typically 2.5-3.5 revolutions per second (15-22 rad/s), and the effective rotation radius is about 2.0 m, yielding theoretical tangential velocities of 25-30 m/s. The measured ejection speed from the kinematic analysis should agree with this value within 10-15%. The optimal release angle is about 42-44 degrees (slightly less than the theoretical 45° due to the release height being above ground level). The predicted throw distance from the projectile equation should be roughly consistent with the actual distance, though discrepancies arise from air resistance and the difference between the release height and ground level. Pointing errors in the video analysis typically limit the velocity accuracy to ±10%.

Scientific questions:

- Why is the ejection speed equal to the tangential velocity of the hammer at the moment of release?
- How does the athlete increase the rotation speed from the first turn to the last?
- Why is the optimal release angle slightly less than 45 degrees?
- What limits the maximum rotation speed the athlete can achieve? What role does the centripetal force play?
- How does the length of the cable affect the throw distance for the same rotation speed?
- Why is conservation of angular momentum important during the spinning phase?

Scientific explanations:

The hammer throw perfectly illustrates the transformation of a circular movement into a linear movement. In this Olympic discipline inherited from Celtic traditions, the athlete rotates a mass (the "hammer", approximately 7.26 kg for men) attached to a cable, creating a circular movement before releasing it.

The linear speed v at the moment of release is theoretically linked to the angular speed ω and to the radius r by the relation v = ω×r. Elite launchers can achieve ejection speeds of 27-29 m/s.

Kinematic analysis makes it possible to experimentally verify this relationship and to identify possible deviations. These differences are mainly explained by the ejection angle: to maximize the range, the optimal angle is not horizontal but around 45° (in the absence of air resistance).

In reality, taking into account aerodynamic resistance and release height, the optimal angle is slightly lower (40-43°). The trajectory after ejection follows a parabola modified by air resistance.

In physical terms, this throw exploits several principles: centripetal force (cable tension) keeps the hammer in circular motion; inertia propels the hammer tangentially upon release; Conservation of angular momentum explains why the athlete accelerates their rotation during the final rounds. FizziQ's kinematic analysis tool allows you to precisely measure these parameters and understand the key factors for optimal performance.

Extension activities:

Frequently asked questions:

Q: The hammer head is blurry in the video during the fast rotation. How can I track it?
R: During rapid rotation, the hammer may appear as a blur. Focus on frames where the hammer is at the extremes of its arc (moving perpendicular to the camera view) where it appears sharpest. Slow-motion video greatly improves tracking quality.

Q: My calculated ejection speed is much lower or higher than expected. What could be wrong?
R: Check your scale calibration carefully, as errors in the reference distance directly affect the calculated speed. Also verify that you are measuring the correct number of frames per revolution to determine the angular velocity.

Q: Why is the rotation radius larger than the cable length?
R: The effective rotation radius includes the athlete's arm length and the distance from the body axis to the hands, which adds approximately 0.6-1.0 m to the cable length of 1.22 m.

Q: Can I analyze a video I recorded at a local athletics event?
R: Yes, but ensure the camera is positioned to view the throw from above or from the side with a clear view of the rotation plane. A fixed camera position with a known reference scale is essential for accurate analysis.