As long as the mass is on the sphere, it has only a tangential velocity ( call it r \ dot \ theta since we're going down the sphere ) and a tangential acceleration provided by gravity.
22.
If you jump in the air, you tend to land again on the same spot, because the Earth has rotated under you, but you have ( almost exactly ) retained the tangential velocity of the spot you jumped from.
23.
If, however, the wheelset is displaced to one side, the diameters of the regions of contact, and hence the tangential velocities of the wheels at the running surfaces are different and the wheelset tends to steer back towards the centre.
24.
Components in the normalized basis are most common in applications for clarity of the quantities ( for example, one may want to deal with tangential velocity instead of tangential velocity times a scale factor ); in derivations the normalized basis is less common since it is more complicated.
25.
Components in the normalized basis are most common in applications for clarity of the quantities ( for example, one may want to deal with tangential velocity instead of tangential velocity times a scale factor ); in derivations the normalized basis is less common since it is more complicated.
26.
The result is that when the air is viewed as if it were a continuous material, it is seen to be unable to slide along the surface, and the air's tangential velocity at the surface goes to practically zero, something known as the no-slip condition.
27.
If you keep to the good old planetary model as worked out by Ernest Rutherford and his ilk, then it's the same reason that the planets don't crash into the sun even though gravity is pulling them in : the tangential velocity is such that the attractive force causes the electrons to orbit.
28.
The speed seen by the rotor blade is dependent on three things : the axial velocity of the fluid, v _ { \ infty } ( 1-a ); the tangential velocity of the fluid due to the acceleration round an airfoil, a'\ omega r; and the rotor motion itself, \ omega r.
