Angular Impulse (HL) (HL IB Physics)

• In linear motion, the resultant force on a body can be defined as the rate of change of linear momentum:

• This leads to the definition of linear impulse:

An average resultant force  acting for a time  produces a change in linear momentum 

• Similarly, the resultant torque on a body can be defined as the rate of change of angular momentum:

• Where:
  • = resultant torque on a body (N m)
  •  = change in angular momentum (kg m² s⁻¹)
  • = time interval (s)

• This leads to the definition of angular impulse:

An average resultant torque  acting for a time  produces a change in angular momentum 

• Angular impulse is measured in kg m² s⁻¹, or N m s
• This equation requires the use of a constant resultant torque
  • If the resultant torque changes, then an average of the values must be used

• Angular impulse describes the effect of a torque acting over a time interval
  • This means a small torque acting over a long time has the same effect as a large torque acting over a short time

Angular Impulse on a Torque-Time Graph

• The area under a torque-time graph is equal to the angular impulse or the change in angular momentum

When the torque is not constant, the angular impulse is the area under a torque–time graph