Question

Topic: Rotational Equilibrium of Torques

1- What are the definitions of:

a) Torque

b) moment of inertia and angular acceleration?

2- How does the moment of inertia relate to probability distributions?

3- how do torques add and what is necessary to establish rotational equilibrium ?

Answer 1

Q1-

a)  

Torque is a measure of the force that can cause an object to rotate about an axis. Just as force is what causes an object to accelerate in linear kinematics,torque is what causes an object to acquire angular acceleration. Torque is a vector quantity.

Torque is the product of moment of inertia and angular acceleration.  

When a torque is applied to an object it begins to rotate with an acceleration inversely proportional to its moment of inertia. This relation can be thought of as Newton’s Second Law for rotation. The moment of inertia is the rotational mass and the torque is rotational force. Angular motion obeys Newton’s First Law. If no outside forces act on an object, an object in motion remains in motion and an object at rest remains at rest.  

b)

moment if inertia-

a quantity expressing a body's tendency to resist angular acceleration, which is the sum of the products of the mass of each particle in the body with the square of its distance from the axis of rotation.

Angular acceleration-

also called rotational acceleration, is a quantitative expression of the change in angular velocity that a spinning object undergoes per unit time. It is a vector quantity, consisting of a magnitude component and either of two defined directions or senses.  

Q2)-

Q3)-

• An object in rotational equilibrium has no net external torque:

               sum of all external torques  =  0
  

  Remember that "rotational equilibrium" may mean that the object is not rotating ... or it may mean that the object is rotating with constant angular velocity.