Rotational Equilibrium - Practice Questions & MCQ

For Translational equilibrium $\sum \vec{F}=0$
And For Rotational equilibrium

$
\sum \vec{\tau}=0
$

- For rotational equilibrium of system the resultant torque acting on it must be zero.
i.e., $\sum \tau=0$
- Various case of equilibrium

$
\text { 1. } \sum \vec{F}=0 \text { and } \sum \vec{\tau}=0
$

Forces are equal and act along the same line.

Body will be in both Translational and Rotational equilibrium.
i.e., It will remain stationary if initially it was at rest.

$
\text { 2. } \sum \vec{F}=0 \text { and } \sum \tau \neq 0
$

Forces are equal and does not act along the same line.

Rotation of body will happen i.e. spinning of body.

$
\text { 3. } \sum F \neq 0 \text { and } \sum \vec{\tau}=0
$

Forces are unequal and act along the same line.

Body will be in Translational motion.
i.e., slipping of body

$
\text { 4. } \sum F \neq 0 \text { and } \sum \tau \neq 0
$

Forces are unequal and does not act along the same line.

Body will be in both Rotation and translation motion.

 i.e. rolling of a body.

• Couple  Force-

1.  A couple is defined as combination of two equal and oppositely directed force but not acting along the same line.

   $
   \text { i.e., } \sum \vec{F}=0 \text { and } \sum \tau \neq 0
   $

   2. Torque by a couple is given by

   $
   \vec{\tau}=\vec{r} \times \vec{F}
   $
    

3.   In case of couple both the forces are externally applied.

4. Work done by torque in twisting the wire is given by 

$W=\frac{1}{2} C \cdot \theta^2$ 

Where C is coefficient of twisting