Rotational Dynamics



[A journalist] asked, ‘Mr. Gandhi, what do you think of modern civilization ?’ And Mr. Gandhi said ‘That would be a good idea’
Mahatma Gandhi – on arriving in England (1930)


 

 

 

where r is the vector from the axis of rotation to the point at which the force is applied, such that r is perpendicular to the axis and theta is the angle between r and F.

 

Note that the torque, angular velocity and angular acceleration are all directed along the axis of rotation.

The magnitude of the torque can be thought of as the product of either

1.      the force and perpendicular distance between the line of action of the force and the turning point (rperpF) or

2.      the distance of the turning point from the point of action of the force and the component of the force perpendicular to this line (rFperp)

 

 Fparallel produces zero torque (theta = 0).  Pushing on directly on the axis of rotation will not create rotation.
 Reversing r or F leaves the magnitude of the torque unchanged, but will reverse its direction (rotation will take place in the opposite direction)

 

Units:  Newton.metre  (N.m)

 Joules are also equivalent to N.m, but you should always use N.m for torque, never Joules.

 

 

Defined in a similar manner to torque,

 

 

where r and theta are defined in exactly the same way as for torque.

 

Units:  kg.m2/s

 

 

 

Taking the definition of angular momentum and differentiating with respect to time we can show that,

 

 

which is the rotational equivalent of  .

 

Extending this to a system of particles,

where L is the vector sum of the angular momenta in the system.


Example Problem


It’s not that I’m afraid to die.  I just don’t want to be there when it happens

Woody Allen – Death (1975)


 

Dr. C. L. Davis
Physics Department
University of Louisville
email: c.l.davis@louisville.edu