Question

I need two example questions with answers for Newton's second law in angular form. I've looked everywhere for example questions and I can't find any. They all have different formulas from my book (which doesn't have practice problems) and when i search Newton's second law in angular form, the only thing that comes up is rotational form, vector form, and Torque. Are these all the same thing? The only thing that my book does to describe this section is prove the formula. Please help!

Answer 1

Newton's Second law in linear motion is F = m*a

   as it would be derived from the the linear momentum

that is we knwo that the linear momentum P = m*v

   rate of linear momentum is Dp/dt = d/dt(mv) = m dv/dt = m*a = F

so F = m*a

and we have in angular motion the analogues to linear momentum in angular motion is anguluar momentum

   L = I*w

now rate of L is dL/dt = d/dt(I*W) = IdW/dt = I*alpha = Torque

   T = I*alpha

torque is analogue with force in linear motion

   so the derivation of Newton's second law in angular motion is

  

           T = I*alpha

if we observe the units of torque as T = I*alpha and T = rF sin theta both are same = kg m2/s2