The speed with which you tug on a toilet roll determines whether a sheet breaks off, or the roll simply unravels.
How it works:
The force applied to the junction between the sheets of a toilet roll is proportional to the rate of change of momentum of your hand as you tug at the end. Thus a sharp tug (large ∆p) is sufficient to surpass the breaking stress of the perforated junction. A lesser tug however, below the breaking stress, will apply a torque to the roll itself; the ensuing rotation unravels the roll.
The instructor breaks several boards with a swift blow of the hand.
What it shows:
The impulse momentum theorem is demonstrated in a most dramatic way by breaking several boards with the blow of your fist. You need not be a karate expert to show how the force of a well executed hammer-fist strike will easily break a stack of five to eight boards. The impulse is given by
impulse = F∆t = ∆mv
The point of the demonstration is: the greater the speed, the smaller ∆t will be and thus the greater the force.