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Why will a person/animal (i.e. dog) continue to travel in a straight line while jumping (assuming initial trajectory to be a straight line) despite twisting motion? (i.e. attempt to twist left/right when viewed from above)? Intuitively I know it is not possible to alter the trajectory without input of an external force, I just don't know how to really explain it.
Answer 1:

The answer to this question lies in Newton's Three Laws of Motion ( read here ).

For this, we employ Law 1 and Law 3:

Law #1: An object at rest stays at rest and an object in motion stays in motion unless acted on by an outside force.

Law #3: Every action has an equal and opposite reaction.

Let's say you're jumping out a window and want to veer left. For this to happen, by Law #1, an outside force must push or pull you to the left. In this scenario the only force source you have to play with are your flailing limbs.

Unfortunately by Law #3, any force exerted by a twist or a limb flail has an equal and opposite force by the rest of your body that will bring your trajectory back to the direction you started. Hence, your net force will always be zero. A fun and less-lethal way to test this out is to find a swivel chair with very little friction, lift your legs off the ground and try to twist and flail your body to rotate either clockwise or counterclockwise. What you will find is that no matter how fast or twisty you move, you will always end up stationary where you started. (You may experience some displacement due to friction)

Please note, everything said above only works in a vacuum and does not take into account the fluid mechanics of the air. Accounting for air pressure, you can DEFINITELY change trajectory mid jump. Skydivers can twist their hands and bodies to move from side to side and rotate. Also birds are very adept at changing trajectory while "jumping" off of things! The "outside force" in this case comes from differences in air pressure, because pressure is a force over an area.


Answer 2:

Once launched in the air with no connection to surface from which to push off of, the center of mass of the system follows a trajectory defined by the gravitational field and the initial conditions when you pushed off. Once in the air and assuming air friction is neglected (good approximation!!) then you may twist this way and throw your arms that way and these "internal motions”. So, the key word you used is EXTERNAL FORCE... then the INTERNAL forces of twisting are compensated by reaction of internal forces since work is not being done by external force action.

Answer 3:

Twisting motion is not force; it's a different physical quantity called torque. Force causes things to move in one direction. Torque causes them to rotate. You can apply torque to yourself even if you can't apply any net force to yourself.

Now, like momentum, angular momentum is also conserved, so if you are going to apply a torque to yourself, you will need to make part of yourself rotate in the other direction. You can test this by sitting in a swivel chair and rotate your body, and you will cause the seat to rotate underneath you in the other direction. Used creatively, you can change the direction you are facing.


Answer 4:

Here's the easiest way for me to understand this: I think about what you need to do to change your trajectory.

Imagine a dog bounding towards you in a zigzag motion. Each time it touches the ground, the dog applies a force to the ground by pushing its feet into the ground. At the same time, the ground will apply an equal and opposite force pushing the dog away. This is an example of Newton's second law of motion.

We can divide the force into two parts. The first part, the normal force, pushes the dog upwards, away from the ground (also called "normal to the ground"). The second part is friction, which pushes the dog along the ground, in the direction opposite his kick. If you look from a bird's-eye view (top down), the frictional force is the important part for changing the dog's trajectory. Of course, the normal force also changes the trajectory by letting the dog leave the ground.

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