Newton's Second Law for Rotation

Newton's second law for rotation, also known as the rotational analog of Newton's second law of motion, describes the relationship between the net torque applied to an object and its resulting angular acceleration.  It states that the net torque acting on an object is directly proportional to the object's moment of inertia and its angular acceleration.  In simpler terms, the law states that the torque applied to an object causes it to undergo angular acceleration, and the magnitude of this angular acceleration is directly proportional to the torque and inversely proportional to the moment of inertia.  The moment of inertia is a measure of an object's resistance to changes in its rotational motion, similar to how mass is a measure of resistance to linear motion.

This law is essential for analyzing rotational motion, such as the motion of spinning objects, rotating machinery, and systems involving rotational forces.  It is widely used in physics, engineering, and various applications involving rotational dynamics and motion control.

 

Newton's Second Law for Rotation formula
\( \tau = I \; \alpha  \)     (Newton's Second Law for Rotation) \( I =  \tau \;/\; \alpha \) \( \alpha =  \tau \;/\; I \)
Symbol	English	Metric
\( \tau \)  (Greek symbol tau) = rotational force	\(lbf\)	\(N\)
\( I  \) = moment of inertia	\(in^4 \)	\(mm^4\)
\( \alpha \)  (Greek symbol alpha) = angular acceleration	\(deg\;/\;sec^2\)	\(rad\;/\;s^2\)