Q.Define angular acceleration and torque. Establish the relation between angular acceleration and torque.
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Start your 14-day free trial to unlock the full solution →Angular acceleration alpha = rate of change of angular velocity; torque = turning effect of a force. Their relation is torque = I alpha (moment of inertia times angular acceleration), the rotational form of F = ma.
Angular acceleration (alpha):
Angular acceleration is defined as the rate of change of angular velocity of a rotating body.
alpha = d(omega)/dt
Its SI unit is radian per second squared (rad/s^2).
Torque (moment of force):
Torque is the turning or rotating effect of a force about an axis of rotation. It is measured by the product of the force and the perpendicular distance of its line of action from the axis:
torque = force x perpendicular distance = F r sin(theta)
Its SI unit is newton metre (N m).
Relation between torque and angular acceleration:
Consider a rigid body rotating about a fixed axis. Take a particle of mass m at distance r from the axis. A tangential force F on it produces a linear (tangential) acceleration a = r alpha.
By Newton's second law: F = m a = m r alpha
The torque of this force about the axis is:
torque on the particle = F r = (m r alpha) r = m r^2 alpha
For the whole body, sum over all particles:
total torque = (sum of m r^2) alpha = I alpha …
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