Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • The vector sum of a system of non-collinear forces acting on a rigid body is given to be non-zero. If the vector sum of all the torques due to the system of forces about a certain point is found to be zero,

The vector sum of a system of non-collinear forces acting on a rigid body is given to be non-zero. If the vector sum of all the torques due to the system of forces about a certain point is found to be zero, does this mean that it is necessarily zero about any arbitrary point?

Answers (1)

The vector sum of all torques due to forces at a point is 0.  Let us assume that \tau be the torque about a point P

Then \tau =\tau _{1}+\tau _{2}+............+\tau _{n}=\sum _{i=1}^{n}\overrightarrow{r_{i}} \times \overrightarrow{F_{i}}=0   (as per question)

Now torque about any other point say A will be given by

\sum _{i=1}^{n}(\overrightarrow{r_{i}}-a) \times \overrightarrow{F_{i}}=\sum _{i=1}^{n}\overrightarrow{r_{i}} \times \overrightarrow{F_{i}}-a\sum _{i=1}^{n}\overrightarrow{F_{i}}

Since a and \sum _{i=1}^{n}\overrightarrow{F_{i}} are not equal to zero. Thus the sum of all torques about any arbitrary point is not 0 necessarily.

 

Posted by

infoexpert23

View full answer

Similar Questions

Latest Question