Recent content by Franco_v

Correction, even if a motor turns the wheel, the wheel will only precess forever if there is no friction in the pivot and no air resistance. In a no friction environment there is no energy required to maintain the precession. But if there is friction, then precession would take energy to...

The first equation only applies to 2D planar motion. The second equation applies to more general 3D motion. Note that in the 2D case the angular momentum (L) is acting in the same direction as the angular velocity (w), so wxL = 0.

The Betz limit commonly applies to wind turbines and to underwater turbines which are made to turn by the bulk movement of water (e.g. tidal power). This theoretical efficiency limit is around 60%, where at most 60% of the wind (or water) kinetic energy is converted to mechanical energy in the...

If the angular acceleration of the disk is zero that means the net torque is zero. In the case of a turbine rotating at constant angular velocity, you have equal and opposite torques acting on both sides of the central shaft. The first torque is the output torque produced by the turbine...

If you were suspended in mid-air with no gravity and were swinging the rope & mass around in a vertical plane, the center of mass of the system would not move, since there are only internal forces acting, and no other forces are acting on the system. This means, however, that your body would be...

I'm currently building a website that focuses on classical mechanics. It covers problems taken from real world applications, so you might find it helpful. Most of the material is first year level, but some is more advanced. I'm not sure I can post the link here, but if you click on my name...

It's ignored because centripetal acceleration does not contribute to torque. It acts in the same direction as the lever arm (r), so it has zero contribution to the torque. Tangential acceleration, however, acts 90 degrees to the lever arm, so it contributes to torque.

It looks correct to me.

Yes, the wheel will always precess about the pivot, as long as it is spinning. So if there was a motor attached to it, it would precess forever. If the wheel is spinning with spin vector in the +y-axis, the precession direction will be into the screen. If the wheel is spinning in the...

When the ball is falling downward at terminal speed the frictional air resistance is acting opposite to the direction of gravity, and the ball doesn't accelerate (since it's moving at constant velocity). Therefore, Friction = mg. Air resistance/friction increases as speed increases. So if the...

The torque is equal to the rate of change of angular momentum (with respect to time). So if the torque acts into the screen, the "change" in the angular momentum vector (pointing in the +y-axis) must be into the screen as well. This means that the direction of rotation must be into the screen...

The first term is the kinetic energy due to the motion of the center of mass. The second term is the kinetic energy due to the rotation of the object (treated as a rigid body). If the body were rotating about the center of mass only (that is, about an axis passing through the center of mass)...