Why we take short steps on slippery surfaces ?
When you walk on slippery surface, if you take big steps you have a tendency to slip. This can be understood by the concept of torque. We can take the hip of the body at the axis about which torque can be measured.
When we take big steps the angle of our leg with the vertical increases. Hence, the component of normal reaction increases which causes the torque due to normal reaction to increase which promotes slipping. Also, the component of friction in the opposite direction decreases which decreases the torque due to friction which again causes slipping as the torque due to the force that can stop slipping is decreasing.
So, it is not recommended to walk with big steps on slippery surface