Physics Vectors & Equilibrium PMDC Conceptual Practice
PMDC Verified Question 11 of 50
Which mathematical condition must be satisfied to guarantee that an object is in rotational equilibrium?
A
\(\Sigma \vec{\tau} = 0\)
B
\(\Sigma \vec{F} = 0\)
C
\(\Sigma \vec{F} = 0\) and \(\Sigma \vec{\tau} = 0\)
D
\(\Sigma \vec{F} > 0\)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option A: \(\Sigma \vec{\tau} = 0\)
Concept:
The specific condition for rotational equilibrium.

Formula:
$$\Sigma \vec{\tau} = 0$$

Solution:
Rotational equilibrium means that the angular acceleration of the body is zero. According to Newton's second law for rotation (\(\Sigma \vec{\tau} = I\vec{\alpha}\)), this state is achieved if and only if the vector sum of all external torques acting on the body is zero.

Why other options are incorrect:
  • B is incorrect because it defines translational equilibrium, not rotational.
  • C is incorrect because while it defines complete equilibrium, the question specifically asks for the condition of rotational equilibrium.
  • D is incorrect because a non-zero net force has no direct bearing on rotational equilibrium unless it creates a torque.

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