Question

If force F=4i^-10j^N is applied at rim of disc at a distance r=-5i^-4j^ from the axis of rotation of the disc find the torque applied

Answer 1

Torque is a vector quantity.  I assume r is in meters. it is not specified.

Torque = r x F        is the cross product of Force and distance between the force and the axis about which the torque is found.

So torque is = ( - 5 i - 4 j) x (4 i - 10 j )
             = -5 * 4 i x i + 5 * 10 i x j - 4 * 4 j x i  + 4 * 10 j x j
             = 0 + 50 k + 16 k + 0
             =  66 k  newton-m
the direction is in the +ve z axis and  magnitude is 66 newton-metres

Answer 2

Answer:

66 N-m

Explanation:

Torque as a function of displacement and Force is given by:-

$\tau = r \times F$

Displacement vector is given by, $r = -5 \hat{i} -4\hat{j}$
Force vector is given by, $F = 4 \hat{i} -10\hat{j} \ N$

To find the torque:-

$\tou = \left[\begin{array}{ccc}i&-j&k\\-5&-4&0\\4&-10&0\end{array}\right]$

This solves to:-

$= [(-5\times-10)-(-4\times4)]\hat{k} \\ \\= [(50)-(-16)]\hat{k} \\ \\= 66 \ \hat{k}$

This means, a torque of 66 N-m will be applied in the positive z-axis.