Question

If you have a non-zero angular acceleration, does that mean that you must also have a non-zero net torque? And how do the net torque vector and the angular acceleration vector compare, in terms of direction?

Answer 1

To understand this, we should compare rotational motion with Newton's second law = F= m*a which is for linear motion.

Torque is equal to Mass moment of inertia times angular acceleration.

Just like Newton's second law of motion which says net force= mass times linear acceleration so just like net force is required to cause a body to accelerate, net torque is also required for a body to accelerate.

Since Net torque= mass moment of inertia times angular acceleration. So if the angular acceleration is non zero, it implies body is under net torque else if angular acceleration is zero, net torque acting on a body must be zero.

Direction- body accelerates in the direction of net force as per Newton's second law. Similarly, the direction of anyangu acceleration will be same as the direction of net torque as given by right hand curl rule.

Hope this helps