Name: Equilibrium of Rigid Body
Uploaded: 2019-07-19
Duration: 7 min 32 s
Description: In this video, we will study the translational as well as rotational equilibrium of a rigid body and two conditions that are necessary to maintain mechanical...

Question

Define angular acceleration and torque. Establish the relation between angular acceleration and torque.

Accepted Answer

Angular acceleration is defined as the rate of change of angular velocity. It is a vector quantity and is represented by $α$ .

$α = \frac{∆ ω}{∆ t}$ where $∆ ω$ is the change in angular velocity and $∆ t$ is the change in time.

Torque is defined as the turning effect of force about an axis of rotation. Torque produces angular acceleration in the body. It is represented by $τ$ .

$τ = F r$ where $r$ is the perpendicular distance between the line of action of force and the axis of rotation and $F$ is the magnitude of force.

Consider a force $F$ acting on an object.

For the tangential component of the force $F_{t}$ , we know that,

$F_{t} = m a_{t} - - - (i)$ where $a_{t}$ is the tangential acceleration.

We know that,

$a_{t} = α r$ where $α$ is the angular acceleration and $r$ is the distance between the line of action of force and the axis of rotation.

Putting the value of $a_{t}$ in equation $(i)$ ,

$F_{t} = m α r$

Multiplying both sides by $r$ , we get,

$F_{t} r = m r^{2} α$

Here $F_{t} r = τ$ and $m r^{2} = I$ where $τ$ is the torque and $I$ is the moment of inertia of a body.

$∴ τ = I α$ .

Define angular acceleration and torque. Establish the relation between angular acceleration and torque.

Important Questions on Systems of Particles and Rotational Motion

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