Abstract: Imagine you are in space with a wheel, and you give it a spin, it should stay in the space place rotating about its center of mass. (Correct me if I am wrong please!) While you are in space, you push a different wheel (along the same vector as the radius) and it moves forward, but it does not spin. Now you are on Earth with both wheels and you give one a spin, the wheel rotates and it moves forward, and the other a push, and it rotates and moves forward.

From my limited understanding of physics, the forces being applied to the wheel on the ground would be gravity, normal force, friction and the angular/linear force you apply to it. Why in space does it spin and not move, or move and not spin, but when in contact with the ground, it spins and moves? Is there a force in play that I have not listed? Also, how do you calculate the linear and angular velocities of the wheels spun and pushed on the ground (And how does the angle of the surface play into this)?


Correct me if I am wrong please! - not a correction but a clarification?

In space there are two possibilities in terms of spinning the wheel.

The first is that you hold on to the axle of the wheel and spin the wheel.
You will spin in the opposite direction.
The centre of mass of the wheel and yourself will not move.
This is illustrated in this video where the direction of spin of wheel (its angular momentum) is changed and the person standing on a "friction free" rotating platform rotates in the opposite direction to conserve angular momentum.

If instead of holding on to the wheel you gave the wheel a push with a line of action not through the centre of mass of the wheel then the wheel will rotate but also the wheel will have a linear velocity ie move way from you in a straight line at constant speed. You will move off in the opposite direction both in terms of your linear velocity but also in terms of your direction of spin.

On the Earth there are extra forces which are acting which modify what happens to the wheel when you push it.

  • $\begingroup$ Okay, so instead of holding the wheel like in the video (in space as well), you let go. Would the wheel go off in a direction like a top? Also, what are the calculations for the push in space that causes rotation? Would it rotate if it was a box? If so, I assume boxes don't rotate on the ground because of collision. $\endgroup$ – Jedi_Maseter_Sam Oct 26 '16 at 12:25
  • $\begingroup$ The wheel would fall. The force whose line of action is not through the centre of mass can be transformed into a force whose line of action is through the centre of mass and a couple as shown here physics.stackexchange.com/a/285167/104696 $\endgroup$ – Farcher Oct 26 '16 at 12:35

You have named all the forces but you have not considered how they affect the motion of the wheel.

In space the wheel keeps spinning in one place or moves in a straight line because of inertia (Newton's 1st Law). When pushed it moves in that direction. When pushed in 2 opposing directions it spins about a point.

When the spinning wheel is placed in contact with the ground, there is a net force on it : the friction force from the ground. Initially the wheel slips against the ground. The friction force slows the rotation and also pushes the wheel forward, accelerating it until the slipping stops. Then the centre has velocity $v=R\omega$ where $R$ is the wheel radius and $\omega$ is the angular velocity of rotation (radians per second).

See : Which force makes a wheel roll down the hill? What causes friction?
Force applied to wheel in pure rolling motion at contact point with road


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