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# The forces and torques acting on the hip joint

## Problem

The gait cycle, or walking cycle, refers the repetitive patterns one makes while ambulating. All of the components of the hip joint shown in Figure 1 are vital to coordinating this process.
Figure 1. Components of the hip joint
There are times during the gait cycle when only one foot is touching the ground, and while in this stance, there are four major forces acting on the leg, as shown in Figure 2: Fm, the force of the gluteal muscles pulling against the greater trochanter of the hip, which is oriented 71 degrees from the horizontal axis; Fr, the reactive force of the acetabulum pressing against the head of the femur which is oriented 77.3 degrees from the horizontal axis; W, the normal force of the floor acting on the bottom of the foot which is equal to a person’s weight; and WL, the weight of the leg which is approximately 0.185 W.
Figure 1. Simplified lever representation of the leg
If the point at the upper left corner of the above diagram is used as the pivot point / fulcrum, then the mathematical equations describing the forces and torques acting on the hip joint are as follows:
Fx = Fm cos 71° - Fr cos 77.3° =0
Equation 1. Force in the x direction
Fy = Fm sin 71° + 0.185 W - Fr sin 77.3° =0
Equation 2. Force in the y direction
∑ τ = 7 x [Fr sin 77.3° - 2.31W]= 0
Equation 3. Torque about the pivot point
During movement, the hip joint slides about 3 cm inside the socket with each step. As the hip joint slides, it experiences a frictional force. The frictional force acting on the hip joint is equal to the product of the reactive force of the acetabulum acting on the femoral head and the coefficient of kinetic friction:
Ff = Fr x μk
Equation 4. Frictional force on the hip joint
Friction is greatly reduced by the synovial fluid which lubricates and fills out the irregularities between the surface of the acetabulum and the surface of the femoral head. The coefficient of kinetic friction of a synovial joint is 0.003. Without the cartilage and synovial fluid to protect from frictional tear, the large forces acting on the hip joint during movement would lead to serious damage.
The coefficient of kinetic friction, μk, for dry bone on bone is 0.3. According to the passage, by what factor does the synovial fluid reduce the coefficient of friction?