Understanding Torque and Inertia: How Does it Affect Motion?

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Torque is directly related to inertia in that it influences the acceleration of an object, similar to how force relates to mass. To overcome the inertia of a balanced wheel and initiate motion, one must apply sufficient torque to counteract both inertia and friction. The moment of inertia quantifies how much torque is needed to achieve a desired angular acceleration. Ignoring friction, the driving torque determines the acceleration, while friction becomes the limiting factor when the motor's torque is insufficient. Understanding these relationships is crucial for effectively calculating the torque required for motion.
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After all this recent talk of torque and power I figure I can post my stupid question of the week:

How does torque relate to inertia?

Say I have a nice balanced wheel that I want to spin. I can calculate the moment of inertia but I'm too old to remember how to figure out how much torque and/or power I need to over come the inertia (and friction) to get it going. I got stalled here in dimensional analysis:

moment of inertia == kg·m²
energy (joules) == kg·m²/s² (Newton-meters)
torque == joules/radian == kg·m²/s² (same as energy but through X degrees of rotation)
From wiki: A torque of 1 N·m applied through a full revolution will require an energy of exactly 2(pi) joules.

So, now ignoring friction, can I figure that the driving torque just influences the acceleration? And then it's only friction that keeps my wheel from spinning when the motor is too small?
 
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schip666! said:
How does torque relate to inertia?
The same way as force relates to mass.
 
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