Static Equilibrium, Torque, Elasticity Lesson 12 by Owen Borville 11.28.2025
Statics is the study of forces in equilibrium. The conditions for equilibrium include motion without linear or rotational acceleration. The first condition for equilibrium is that the net external force on the system must be zero, ΣF(net) = 0.
The second condition for equilibrium is that the torques are balanced, or the sum of external torques from external forces is zero (Σ𝜏= 0) Torque is the rotational equivalent of a force in producing a rotation and is defined to be 𝜏 (torque) = rFsin θ, where r is the distance from the pivot point to the point where the force is applied, F is the magnitude of the force, and θ is the angle between F and the vector directed from the point where the force acts to the pivot point. The perpendicular lever arm r ⟂ is r ⟂ = r sin θ so that 𝜏 = r ⟂ F.
Both conditions of equilibrium must be met in order for an object to be in equilibrium. Free body diagrams can be used to account for all external forces and torques acting on a body.
The perpendicular lever arm r ⟂ is the shortest distance from the pivot point to the line along which F acts. The SI unit for torque is the newton meter (N * m).
The second condition necessary to achieve equilibrium is that the net external torque on a system must be zero: net 𝜏 = 0. Counterclockwise torques are positive, and clockwise torques are negative (just like shower faucet knobs).
A body is in equilibrium when it is in uniform motion (linear or rotational) or at rest. When a body does not move or rotate, the body is in static equilibrium.
A system is in stable equilibrium if, when displaced from equilibrium, it experiences a net force or torque in a direction opposite the direction of the displacement. A system is in unstable equilibrium if, when displaced from equilibrium, it experiences a net force or torque in the same direction as the displacement from equilibrium. A system is in neutral equilibrium if its equilibrium is independent of displacements from its original position.
Applications of statics include structural design of buildings, bridges, cranes, dams, arches, biomechanics of human posture, muscle and joint forces, ergonomics of furniture, and robotics.
Simple machines in physics can increase the force that humans apply, usually for a distance. A simple machine has few or no moving parts that changes direction or magnitude of a force to make work easier. Mechanical advantage is the ratio of output to input forces for any simple machine. Mechanical advantage is used to multiply force, often by increasing the distance over which the force is applied. Simple machines modify force and motion to perform work. Six classical simple machines are the inclined plane, lever, wedge, pulley, screw, and wheel and axle.
Statics is important to understand strains in human and animal muscles and bones. Many lever systems in the body have mechanical advantage of significantly less than one, because many muscles are attached close to joints. Good posture is when a person's center of gravity is directly above the pivot point in the hips, in order to avoid back strain and damage to disks.
Deformation is an external force on an object (or medium) that causes a change in size and shape. Stress is the strength of the forces that cause deformation. Stress is measured in SI units of pressure (pascal). Strain is the extent of deformation under stress and is dimensionless.
During small stress, the relationship between stress and strain is linear. stress = (elastic modulus)*(strain). The elastic modulus is the proportionality constant in this linear relation.
Tensile or compressive strain is the response of an object to tensile or compressive stress. This elastic modulus is called Young's modulus. Tensile or compressive stress causes elongation or shortening of the object and is due to external forces acting along only one direction perpendicular to the cross section.
Young's modulus (Y) = (tensile stress)/(tensile strain) = F/A (L0/ΔL) or FL0/AΔL, where A is the cross-sectional area and L is the length
Bulk strain is the response of an object or medium to bulk stress. This elastic modulus is called the bulk modulus. Bulk stress causes a change in the volume of the object or medium and is caused by forces acting on the body from all directions, perpendicular to its surface. Compressibility of an object or medium is the reciprocal of its bulk modulus.
Bulk modulus (B) = (bulk stress/bulk strain) = -ΔP(V0/ΔV), where P is pressure and V is volume
Shear strain is the deformation of an object or medium under shear stress. This elastic modulus is the shear modulus. Shear stress is caused by forces acting along the object's two parallel surfaces. Shear modulus (S ) = (shear stress/shear strain) = F/A(L0/Δx) or FL0/AΔx, where A is the force applied area, x is the amount of deformation
Elastic objects come back to their original shape and size when the stress disappears. In elastic deformations with stress values lower than the proportionality limit, stress is proportional to strain. When stress goes beyond the proportionality limit, the deformation is still elastic but non-linear up to the elasticity limit.
Plastic behavior is when stress is larger than the elastic limit in an object or material. In the plastic region, the object or material does not come back to its original size or shape when stress disappears but acquires a permanent deformation. Plastic deformation ends at the breaking point.
Statics is the study of forces in equilibrium. The conditions for equilibrium include motion without linear or rotational acceleration. The first condition for equilibrium is that the net external force on the system must be zero, ΣF(net) = 0.
The second condition for equilibrium is that the torques are balanced, or the sum of external torques from external forces is zero (Σ𝜏= 0) Torque is the rotational equivalent of a force in producing a rotation and is defined to be 𝜏 (torque) = rFsin θ, where r is the distance from the pivot point to the point where the force is applied, F is the magnitude of the force, and θ is the angle between F and the vector directed from the point where the force acts to the pivot point. The perpendicular lever arm r ⟂ is r ⟂ = r sin θ so that 𝜏 = r ⟂ F.
Both conditions of equilibrium must be met in order for an object to be in equilibrium. Free body diagrams can be used to account for all external forces and torques acting on a body.
The perpendicular lever arm r ⟂ is the shortest distance from the pivot point to the line along which F acts. The SI unit for torque is the newton meter (N * m).
The second condition necessary to achieve equilibrium is that the net external torque on a system must be zero: net 𝜏 = 0. Counterclockwise torques are positive, and clockwise torques are negative (just like shower faucet knobs).
A body is in equilibrium when it is in uniform motion (linear or rotational) or at rest. When a body does not move or rotate, the body is in static equilibrium.
A system is in stable equilibrium if, when displaced from equilibrium, it experiences a net force or torque in a direction opposite the direction of the displacement. A system is in unstable equilibrium if, when displaced from equilibrium, it experiences a net force or torque in the same direction as the displacement from equilibrium. A system is in neutral equilibrium if its equilibrium is independent of displacements from its original position.
Applications of statics include structural design of buildings, bridges, cranes, dams, arches, biomechanics of human posture, muscle and joint forces, ergonomics of furniture, and robotics.
Simple machines in physics can increase the force that humans apply, usually for a distance. A simple machine has few or no moving parts that changes direction or magnitude of a force to make work easier. Mechanical advantage is the ratio of output to input forces for any simple machine. Mechanical advantage is used to multiply force, often by increasing the distance over which the force is applied. Simple machines modify force and motion to perform work. Six classical simple machines are the inclined plane, lever, wedge, pulley, screw, and wheel and axle.
Statics is important to understand strains in human and animal muscles and bones. Many lever systems in the body have mechanical advantage of significantly less than one, because many muscles are attached close to joints. Good posture is when a person's center of gravity is directly above the pivot point in the hips, in order to avoid back strain and damage to disks.
Deformation is an external force on an object (or medium) that causes a change in size and shape. Stress is the strength of the forces that cause deformation. Stress is measured in SI units of pressure (pascal). Strain is the extent of deformation under stress and is dimensionless.
During small stress, the relationship between stress and strain is linear. stress = (elastic modulus)*(strain). The elastic modulus is the proportionality constant in this linear relation.
Tensile or compressive strain is the response of an object to tensile or compressive stress. This elastic modulus is called Young's modulus. Tensile or compressive stress causes elongation or shortening of the object and is due to external forces acting along only one direction perpendicular to the cross section.
Young's modulus (Y) = (tensile stress)/(tensile strain) = F/A (L0/ΔL) or FL0/AΔL, where A is the cross-sectional area and L is the length
Bulk strain is the response of an object or medium to bulk stress. This elastic modulus is called the bulk modulus. Bulk stress causes a change in the volume of the object or medium and is caused by forces acting on the body from all directions, perpendicular to its surface. Compressibility of an object or medium is the reciprocal of its bulk modulus.
Bulk modulus (B) = (bulk stress/bulk strain) = -ΔP(V0/ΔV), where P is pressure and V is volume
Shear strain is the deformation of an object or medium under shear stress. This elastic modulus is the shear modulus. Shear stress is caused by forces acting along the object's two parallel surfaces. Shear modulus (S ) = (shear stress/shear strain) = F/A(L0/Δx) or FL0/AΔx, where A is the force applied area, x is the amount of deformation
Elastic objects come back to their original shape and size when the stress disappears. In elastic deformations with stress values lower than the proportionality limit, stress is proportional to strain. When stress goes beyond the proportionality limit, the deformation is still elastic but non-linear up to the elasticity limit.
Plastic behavior is when stress is larger than the elastic limit in an object or material. In the plastic region, the object or material does not come back to its original size or shape when stress disappears but acquires a permanent deformation. Plastic deformation ends at the breaking point.