Comparing linear and circular motion we can see that moment of inertia represents mass and torque represents force. So the product change in the circular momentum per unit time is torque.
Circular momentum is the product of moment of inertia and circular velocity.
Torque is vector energy and moment is the time integral of force.
Imagine a pendulum, if you will. The longer a pendulum is, the longer it will take to make a full cycle. The converse is also true; if a pendulum is shorter, it will take less time to make a full cycle. The answer lies in the gravitational potential energy of the system, and the moment of inertia of the pendulum. Given a fixed mass at the end of a string with negligible mass, it is apparent that the longer the string is, the greater its moment of inertia (inertial moment is roughly analogous to the inertia of a stationary object). With only a fixed amount of gravitational potential energy to drive the pendulum, the one with a larger moment of inertia will travel slower.
It can be done, but it would require taking an integral for the moment of inertia of each particle of the disc... something i don't have the time to do right now ^^;
Rotational speed is measure in terms of rotations per second (not necessarily per second, you could use other units of time, but let it be per second) whereas torque is measured in newtons, which are units of force. The amount of rotations per second that you get per newton of applied force depends upon the inertia (measured as "moment arm" for a rotating body) that the force has to overcome.
Torque is equal to friction force (F) * radius (r). Torque is also equal to moment of inertia (I) * Angular acceleration (a). Angular acceleration is equal to rotational velocity * 2Pi/time, which is 2 seconds. So, F = IRa/r, or 45.63 Newtons
Force times time is Impulse Inertia is mass
"Rate of change" means that you divide something by time ("per unit time" or "per second"), so you would use the units of angular momentum, divided by seconds.I am not aware of any special name for this concept.
Inertia is basically resistance of an object to change it's state of motion. The force or moment of inertia each object has is based on one of Newton's classic laws of motion: Force = Mass X Acceleration. It would be dependant on the moment of inertia of either vehicle at the time. A 20000 kg plane moving at 1m per second has the same force as a 2000 kg moving at 10m per second.
I am not sure whether Newton actually stated this law... It's more like an analogy, or equivalent. It is still valid, though. Newton's Second Law for linear movement: force = mass x acceleration. The equivalent for rotational movement: torque = (moment of inertia) x (angular acceleration). Keeping it simple: acceleration = change in velocity/time for change. Velocity is a vector having both size and direction, thus any change in direction changes velocity. Not its magnitude, just its direction. A change in velocity with time means the object is accelerating. To do this a force must be applied perpendicular to the direction of the velocity vector to pull the object round into a circle. F=ma applies, therefore.
The same as the acceleration rate. Measure the speed at one moment of time, measure the speed at another moment of time, calculate the difference, divide by the time elapsed.
Long balancing poles have large rotational inertia, therefore the effect of net torque (if any) appears over large time. This much time is sufficient enough for the person to adjust the length of the pole so that the effect of torque can be corrected, while moving forward on the tightrope.
There are two laws about inertia. The First Law has no formula. It is just a statement that says "an object will continue at constant velocity ,or at rest, until a net force acts on it". This property that requires a force to change its state of motion (or rest) is called the object's "inertia". The Second Law is a formula that describes how an object will move when a net force acts on it. The formula is F = ma. Where, F, is the force and , a , is the objects acceleration. And , m , is the objects mass, which is a measure of the object's inertia. So you could write the formula as a = F/m and in this way you see if the object's mass (inertia) is increased then in order to get the same acceleration you must increase the force. These two laws describe how an object's inertia ,or mass, resists changes in its motion.