full lifts with both legs. He then continues to lie on the floor with his left leg pointing straight up (bottom of foot facing up so that his left leg is perpendicular to the floor) and his right leg resting on the floor. If Logan allows his leg to fall freely until it hits the floor what is the tangential speed of his left foot just before it hits the floor. Assume his leg can be treated as a uniform rod of length 0.85 m long that pivots freely about the hip.
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.
Given:
Length of the leg 'L' = 0.85 m
Leg can be treated as an uniform rod.
The falling of leg towards floor is an free fall.
Left leg is perpendicular to the floor.
Refer the diagram :
In the diagram we can see,
- Leg is perpendicular to floor.
- When this will be allowed to fall freely on floor it will have some rotational kinetic energy ( RKE ) with angular speed ω.
- Since leg can be treated as uniform rod then using concept of center of mass we know its entire mass can be assumed to be concentrated at h. And h = L / 2.
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