An electric motor applies a torque of 700 N·m to an aluminum shaft, triggering a stable rotation. Two pulleys, B and C, are subjected to torques of 300 N·m and 400 N·m, respectively. The modulus of rigidity is provided as 25 GPa. With the knowledge of the length and diameter of each segment, the twist angle between the two pulleys can be computed. First, a section cut is made between pulleys B and C, and the cut cross-section is analyzed using a free-body diagram. Given that the torque...

A rigid body's rotation around a fixed axis makes every point within it trace a circular path around a specific line or point. The term given to this type of spinning is defined by the angular position, symbolized by the angle θ. This angle is gauged from a static reference line to the revolving object. From this angular position, any variation is referred to as angular displacement, denoted by dθ. The extent of this displacement can be calculated in degrees, radians, or...

The femur is the body's longest and strongest bone spanning the thigh region. Its head articulates with the acetabulum of the hip bone to form the hip joint. A minor indentation on the medial side of the femoral head, called the fovea capitis, serves as the site of attachment for the ligament of the head of the femur. This weak ligament spans the femur and acetabulum and supports the hip joint. The narrowed region below the head is the neck of the femur. The inclination angle between the...

The ankle is formed by the talocrural joint (crural = leg). It consists of the articulations between the talus bone of the foot and the distal ends of the tibia and fibula of the leg. The superior aspect of the talus bone is square-shaped and has three areas of articulation. The top of the talus articulates with the inferior tibia. This is the portion of the ankle joint that carries the body weight between the leg and foot. The sides of the talus are firmly held in position by the articulations...

The tibia is the main weight-bearing bone of the lower leg. It is larger than the fibula with which it is paired. The tibia is also the second longest bone in the body and is located right below the skin. The proximal end of the tibia forms the medial and the lateral condyle, which articulates with the condyles of the femur to form the knee joint. Between the articulating surfaces is the irregular elevated area known as the intercondylar eminence that serves as the inferior attachment point for...

In mechanics, when one observes a rigid body in rotational motion with constant angular acceleration, it is possible to establish equations for its rotational kinematics. This process resembles how linear kinematics are dealt with in simpler motion studies.
For instance, imagine a point A on a rigid body engaged in circular motion. The translational velocity of this particular point can be calculated by taking the time derivatives of the displacement equation, which essentially measures the...