Rotational Equilibrium MCQ - Practice Questions with Answers

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

And For Rotational equilibrium $\sum \vec{\tau}=0$Í

• - For rotational equilibrium of the system the resultant torque acting on it must be zero.

  $$
  \text { i.e., } \sum \tau=0
  $$

  - Various cases 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 do not act along the same line.

  Rotation of the body will happen i.e. spinning of the 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 do 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 a combination of two equal and oppositely directed forces but not acting along the same line.

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

2. A torque by a couple is given by

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

3. In the case of a 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 the coefficient of twisting