What is torque, really? Can it be determined for a point on a circle that is away from its center of the rotation axis by a radius “r”?

Nov 2019

Let's picture a Rolling without slipping Wheel, that constantly accelerates. radius of a wheel/circle is rr.

Basically any wheel of a vehicle is rotating around its fixed axis - AoR -(axis of rotation)

Most of the times wheels have this AoR perfectly in the center of the circle/wheel/cylinder. What I want to understand is how can we describe the torque of such a wheel?

Because as I understand we could go about finding torque for the center of the circle - point O.

I am not sure if it's possible to find the torque for the point P, that is point on a line tangent to the circle on the surface level.
Oct 2017
The torque is a vector that lies along the axis of rotation (i.e. goes through O). Since P is not the position of the axis of rotation, it doesn't make sense to ask what the torque is at that point.

If you're wondering about how resistance affects rotating objects, the friction at point P applies a force \(\displaystyle F_f\) on the wheel. This force applies a resisting torque, which is also a vector along the axis of rotation, but opposite to the applied torque on the wheel. This torque has magnitude equal to:

\(\displaystyle \tau_f = F_f \times r\).

The vector sum of the torques gives the net torque:

\(\displaystyle \tau = \tau_{drive} + \tau_f\)

with \(\displaystyle \tau_f\) negative, which can then be used to determine whether there is an angular acceleration (or not). Since your situation has a constant acceleration, a, the angular acceleration will also be constant.
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