Lecture 12: Non-Conservative Forces - Resistive Forces - Air Drag - Terminal Velocity

author: Walter H. G. Lewin, Center for Future Civic Media, Massachusetts Institute of Technology, MIT
recorded by: Massachusetts Institute of Technology, MIT
published: Oct. 10, 2008,   recorded: October 1999,   views: 35089
released under terms of: Creative Commons Attribution Non-Commercial Share Alike (CC-BY-NC-SA)

See Also:

Download Video - generic video source Download mit801f99_lewin_lec12_01.m4v (Video - generic video source 107.0 MB)

Download Video - generic video source Download mit801f99_lewin_lec12_01.rm (Video - generic video source 108.6 MB)

Download Video Download mit801f99_lewin_lec12_01.flv (Video 107.7 MB)

Download Video Download mit801f99_lewin_lec12_01_352x240_h264.mp4 (Video 149.2 MB)

Download Video Download mit801f99_lewin_lec12_01.wmv (Video 438.9 MB)

Download subtitles Download subtitles: TT/XML, RT, SRT

Help icon Streaming Video Help

Related Open Educational Resources

Related content

Report a problem or upload files

If you have found a problem with this lecture or would like to send us extra material, articles, exercises, etc., please use our ticket system to describe your request and upload the data.
Enter your e-mail into the 'Cc' field, and we will keep you updated with your request's status.
Lecture popularity: You need to login to cast your vote.



1. Resistive and Drag Forces:

Resistive forces have a viscous term that is linear in velocity; it is temperature sensitive and reflects the stickiness of the medium. In addition they have a pressure term that is proportional to the speed squared and the fluid's density. Resistive forces are always in the direction opposite the velocity. The resistive force grows as the speed increases. Therefore, a falling object in air (or in a liquid) will reach a terminal velocity.

2. Two Regimes and the Critical Velocity:

The drag, or resistive force has two terms; the viscous and pressure terms. They are equal in magnitude at a "critical" speed. At speeds much smaller than this, the terminal speed for spherical objects (all with the same density) increases as the radius squared of the objects. At speeds much larger than the critical speed, the pressure term dominates and the terminal velocity increases as the square root of the radius.

3. Measurements with Steel Balls in Syrup:

Small ball bearings are dropped in Karo Corn Syrup. Professor Lewin explains why the terminal velocity of the ball bearings will vary with the radius squared. He conducts measurements to validate this.

4. Reaching Terminal Velocity in the Blink of an Eye:

When the ball bearings are dropped in the syrup, their speeds at first increase. It is shown that they reach their terminal velocity very fast.

5. Air Drag and the Pressure Term:

The air drag on almost all objects that fall in air from a considerable height (raindrops or sky divers) is dominated by the pressure term. Thus the terminal speed increases with the square root of the radius of spheres with given density. If you want to calculate the time it takes to reach this terminal speed, you have to include both the v and v-squared terms. Lewin's graduate student, Dave Pooley, solved the equation numerically, and a measurement is made with a balloon (filled with air) that is dropped from a height of about 3 meter.

6. Numerical Calculations of Air Drag Examples:

A pebble, dropped from a height of 475 meters (the Empire State Building), reaches a terminal speed of about 75 miles per hour in 5-6 seconds. Professor Lewin also discusses the contribution of air drag to the quantitative experiments done earlier in the course with falling apples.

7. Resistive Forces and Trajectories:

Air drag will result in an asymmetric trajectory for an object thrown up in the air. The resistive force is about the same for a tennis ball as for a styrofoam ball of the same radius, but the resistive force has a much more dramatic effect on the lighter ball's trajectory.

Link this page

Would you like to put a link to this lecture on your homepage?
Go ahead! Copy the HTML snippet !

Reviews and comments:

Comment1 Davor form VideoLectures, December 18, 2017 at 10:27 a.m.:

Hi all!

We have translated this entire course for you from English into 11 languages.

Check this video and give us some feedback in this short survey https://www.surveymonkey.co.uk/r/6DMBC3Q

Comment2 kushal, December 5, 2019 at 7:30 p.m.:

he is an outstanding professor I wanted to meet him

Write your own review or comment:

make sure you have javascript enabled or clear this field: