# How does torque affect speed?

torque is a twisting force that causes an object to rotate. Rotation is the speed at which an object spins around its axis.

torque is a function of both anguar acceleration (alpha) and rotational inertia ("I") --> torque = "I" (alpha)

"I" is a measure of an objects resistance to rotation. Big "I" means an object rotates slowly; small "I" means an object rotates faster.

"I" = mr^2 --> therefore, as the radius of a rotating object decreases, it's resistance to rotation decreases and it rotates faster. Along the same lines, if an object's mass (more technically an object's distribution of mass) decreases it rotates faster. Since the radius in the function is squared, a decrease in radius gets you more bang for your buck than a decrease in mass.

Conversely, objects like hoops rotate more slowly since their radii are large and their mass is distributed along the outer edge of the hoop.

angular acceleration (alpha) = angular-velocity/time --> therefore, as the angular velocity increases, the angular acceleration increases and the object rotates faster.

Both these factors -- alphs and "I" -- directly affect torque and therefore affect the speed at which an object rotates.