Question

A particle of mass m moves on the path given by r=ia.coswt+j.bsinwt.calculate the torque about the origin

Answer 1

We have ,

r = i.a.coswt + j.bsinwt

we know that

T = r x F

where x is the vector multiplication.

Since mass = m and gravity = g

hence force = mg

Since this force is acting in downwards direction, so F in vector form is  

F = - j mg

Hence ,  

T = (i. a coswt + j. bsinwt) x (-j mg)

= - mgacoswt(i x j) - mgbsinwt(jxj)

Since i x j = k and j x j = 0

Therefore, T = - mga cos wt . k