Question

the angular momentum J of a particle is given as J=8t^4i-2t^2j+12t^3k,find the torque at t=1.
(i should confirm that it is 8t the power of 4 likewise take others powers also)

Answer 1

The torque is

$$\tau=\frac{dJ}{dt}$$

$$\tau=\frac{d}{dt} (8t^4\bold{i}-2t^2\bold{j}+12t^3\bold{k})$$

$$\tau= (8(4)t^3\bold{i}-2(2)t\bold{j}+12(3)t^2\bold{k})$$

$$\tau(1)= 32\bold{i}-4\bold{j}+36\bold{k}$$