Study Notes on Rotational Equilibrium and Torque

Rotational Equilibrium

• Objects remain in rotational equilibrium if their center of mass is above the area of support.

• Factors affecting rotational equilibrium explain techniques in sports (gymnastics, skating, diving).

Torque

• Torque is the turning force causing rotational acceleration.

• Mechanical equilibrium requires both:

  • Sum of forces (ΣF) = 0

  • Sum of torques (Σtorques) = 0

• Torque formula: $\tau = F \times d$, where (d) is the distance (lever arm) from the axis.

Balanced Torques

• Balance achieved when clockwise and counterclockwise torques are equal:

  • $(F \cdot d)<em>{cw} = (F \cdot d)</em>{ccw}$

• Center of mass (CM) is crucial; heavier objects closer to pivot, lighter ones farther from pivot.

Center of Mass

• The CM is the average position of mass in an object, affecting its motion.

• Symmetrical objects have a CM at the geometric center; irregular ones have the CM towards the heavier end.

Center of Gravity

• CM and center of gravity act similarly except in large objects where gravity varies.

• An object remains upright if its CM is above its support base.

Stability

• Stability influenced by the location of CM relative to the support base.

• Objects in stable equilibrium require work to raise CM for toppling; unstable equilibrium lowers CM upon displacement.

Key Concepts

• Increasing lever arm or applying torque can make an object easier to turn.

• An object’s stability increases with a lower center of gravity.

• An object topples when its CM extends beyond its area of support.

• The position of a person's CG varies with body orientation and affects balance.