uring a concentric loading of the quadriceps muscle in the upper leg, an athlete extends his lower leg from a vertical position (see figure (a)) to a fully extended horizontal position (see figure (b)) at a constant gular speed of 30.0° per second. Two of the four quadriceps muscles, the vastis intermedius and the rectus femoris, terminate at the patellar tendon which is attached to the top of the tibia in the lower leg. The stance from the point of attachment of the patellar tendon to the rotation axis of the tibia relative to the femur is 4.10 cm in this athlete. a a) The two quadriceps muscles can exert a maximum force of 200 N through the patellar tendon. This force is applied at an angle of 25.0° to the section of the tibia between the attachment point and the rotation axis. What is the torque (in N · m) exerted by the muscle on the lower leg during this motion? (Enter the magnitude.) N.m b) What is the power (in W) generated by the athlete during motion? c) Modeling the lower leg as a thin rod with mass 4.10 kg and length 40.0 cm, what is the kinetic energy (in J) of the lower leg during the motion?
Angular Momentum
The momentum of an object is given by multiplying its mass and velocity. Momentum is a property of any object that moves with mass. The only difference between angular momentum and linear momentum is that angular momentum deals with moving or spinning objects. A moving particle's linear momentum can be thought of as a measure of its linear motion. The force is proportional to the rate of change of linear momentum. Angular momentum is always directly proportional to mass. In rotational motion, the concept of angular momentum is often used. Since it is a conserved quantity—the total angular momentum of a closed system remains constant—it is a significant quantity in physics. To understand the concept of angular momentum first we need to understand a rigid body and its movement, a position vector that is used to specify the position of particles in space. A rigid body possesses motion it may be linear or rotational. Rotational motion plays important role in angular momentum.
Moment of a Force
The idea of moments is an important concept in physics. It arises from the fact that distance often plays an important part in the interaction of, or in determining the impact of forces on bodies. Moments are often described by their order [first, second, or higher order] based on the power to which the distance has to be raised to understand the phenomenon. Of particular note are the second-order moment of mass (Moment of Inertia) and moments of force.
During a concentric loading of the quadriceps muscle in the upper leg, an athlete extends his lower leg from a vertical position (see figure (a)) to a fully extended horizontal position (see figure (b)) at a constant angular speed of 30.0° per second. Two of the four quadriceps muscles, the vastis intermedius and the rectus femoris, terminate at the patellar tendon which is attached to the top of the tibia in the lower leg. The distance from the point of attachment of the patellar tendon to the rotation axis of the tibia relative to the femur is 4.10 cm in this athlete.
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