calculation torque help!

[shelly89]

Hello,

Can someone please just clarify my notes for me, i really cant understand how my teacher gets \(\displaystyle j = - cos \phi \hat{\phi}-sin \phi \hat{r}\)


I have attached the question and solution, but i have no idea how to work out j, the unit vector in terms of phi and r, please can someone show me how to work this out from first principles?

 

[EatMyPossum]

No solution, just a hint

Hi,

I have to little time to work this out for you, maybe later. I suggest you start by examining the relation between j and phi. for instance, if phi is 0, sin(phi) is 0, cos(phi) is 1, so than j = -phi(hat). do this for phi is pi/2, pi and 3/2 pi, and you can probably derive the definitions of phi and j, given that rhat is away from the middle, and phihat is perpendicular to rhat

 

[Dale10101]

Consider this

Hello,

Can someone please just clarify my notes for me, i really cant understand how my teacher gets \(\displaystyle j = - cos \phi \hat{\phi}-sin \phi \hat{r}\)


I have attached the question and solution, but i have no idea how to work out j, the unit vector in terms of phi and r, please can someone show me how to work this out from first principles?

One difficulty is that your diagram does not denote the direction of unit vectors r and phi. I include a diagram and my interpretation of what is going on. Hope it helps, good luck.