Rotational dynamics
Physics Assignment Help & Live Online Tutoring From Our Expert Physics Tutors
 |
Torque: |
 |
| |
The force is the cause of linear motion. Similarly, torque is the cause of rotational motion. Thus,
torque plays similar role as that of force in rotational motion. Basically, torque is a measure of how
much force acting on an object causes that object to rotate. The torque on a particle (which has the
position r in some reference frame) can be defined as the cross product of the position vector and
the force acting on the object:
More generally, torque can be defined as the rate of change of angular momentum,
where, L is the angular momentum vector.
Rotational Inertia and Newton’s Second Law:
uniform speed until and unless it is acted by an external torque.
The moment of inertia of a point mass rotating about a known axis
is defined by,
where m is the mass, and r is the (perpendicular) distance of the point mass to the axis of rotation.
The moment of inertia is additive in nature. Thus, for a rigid body consisting of
N point masses mi
with distances ri to the rotation axis, the total moment of inertia is given as the sum of the point-
mass moments of inertia:
Now the equation for Newton's second law is given by,
∑F = m a
Or ∑r × F = m r × a = m r × (α × r)
Or ∑r × F = m α(r•r) − r(r•α)
= m α r2 − 0 = mr2 α
Or ∑τ = I α
Thus, the total torque is the product of moment of inertia of the rigid body and angular acceleration.
|
|
 |
|
 |
Submit your homework or assignment.
