h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Velocity v = distance covered during time t, v = d(r)/d(t), m/s. Acceleration a = rate of change of velocity, a = d(v)/d(t), m/s^2, also a = v d(v)/d(r), and a = d^2(v)/d(t)^2 = r/t^2. Force = a * m, N. Work = Force applied * displacement * cos of the angle between them,J. Or it could be W = r * force [cos(theta) + sin(theta)],j ? An object with rotational speed(going around a circle) v = 2*pie*r/t = w*r, then a = d(v)/d(t) = 2*pie*r/t^2, m/s^2, force = m*a, N, and energy = force*r, J. The snag with this is, the speed of the object going around the circle, is at a constant value & remains the same no matter which time period d(t) is chosen? The object may have angular momentum but does it really have acceleration, force and hence kinetic energy, especially if w, r and m are all kept at constant values? The same goes for E(kinetic) = L*w/2 or [I*w^2]/2, J? Surely an object in orbit has potential energy = m*v^2, or m*g*h, Joules.

Sorry for the confusion in the previous posting, the amount (scalar) angular energy is dependent on the strength of the tethering force. Usually gravity, but other short range forces can be much stronger. For gravity use g*m*h, while for the much stronger tethering forces its probably better to use E = l*w/2, Jules. I`m still not convinced by arguments that say that an orbiting object`s energy is kinetic, I`d much rather believe that it`s stored potential energy.

Angular momentum units are kg m^2 s^-1, and angular energy(l/t) should be in units of kg m^2 s^-2, but this is actually the same units as used for Torque! Hence my confusion, especially compounded by centrifugal and centripetal forces, when multiplied by the radius also give units of kg m^2 s^-2 ? Even worse is Angular Energy = l w/2, or I*w^2 which when expanded = m[r^2][2*pie^2]*s^-2, kg m^2 rad^2 s^-2, do you just pretend that the 2 times radian squared term has no effect?

If Torque is the angular equivalent of force, why is angular energy not the equivalent to the integral of torque with respect to displacement, hence Angular energy = m(r^3)/t^2, kg m^3 s^-2 ? After all rotating objects do tend to have volume! Is the use of omega angular frequency "w", a way of approximating (pretending to be) volume?

Tried ask.com, found out that an angle in radian units is the ratio of distance (l) around the circumference to the radius. Also Torque is force applied to a point on the circumference. Torque = Force x r sin theta, N.m/rad, it could add energy or take it away from an already rotating object, or the object might just move a certain distance around the circumference. Torque = [m*r^2 /t^2]*r/l, N.m.rad^-1. Hence E(torque) = Torque*angle theta, N.m. or (N.m /rad)*rad.

Apparently rotational energy is kinetic because its keeping the object going around the circumference with constant angular momentum. Velocity v = w*r = theta*r /t = (l /r)(r /t) = l/t, circumferential length divided by time, m/s. E(rotation) = I*w^2 /2, E(r) = I*(l/rt)^2 /2, j. And E(r) = m*l^2 /t^2, j.

Found a useful website, about rotational motion "www.sparknotes.com". The shape of the rotating object alters its Moment of Inertia "I", a rotating ring`s I = m*r^2, while a disc`s I = 0.5m*r^2 and a sphere`s I = 0.4m*r^2.

The rotating objects shape dictates which moment of inertia equation is used(best guess), or work it out by first deciding if its mass density is; 1d(lambda,kg/m), 2d(sigma,kg/m.sq.) or 3d(rho,kg/m^3). Since the moment of inertia "I", is obtained by the integration of radial length squared with respect to mass. The trick is, replace mass with mass density(of the chosen type) times delta(incremental) radial length, and do the integration. Easier still because the object is spinning, let angular momentum, L = m*((l/2p)^2)*2p/t = (m*l^2)/(2p*t), where rotational length, l = 2*pie*r, r = radial length, m = mass, t = time. Might Get around the problem..what if density is not a constant?

Checked in "Physics for scientists and engineers,ISBN:0-7167-0809-4", a hollow ring`s, I = M*r^2, since density at a point is M/r^0 = M,kg.

Surely as the ring is made ever thiner, density takes off to infinity, so why is I = M*r^2 and not infinity?

October 3rd 2009 New scientist magazine has an article about the Stratwarm, which is a kind of weather event that happens within the stratosphere. As this vortex of cold air above the north pole wobbles around it becomes unstable breaking into smaller vortexes, letting warmer air in, which seems to somehow calm things down, re-establishing the original vortex?

Since an eastward flowing jet stream in the northern hemisphere develops wiggles to the south & north (Rossby waves) as it rises & falls passing over highs & lows, do jet aircraft also wiggle?