A 60 kg person, running quickly at 5.5 m/s sees a rope swing hanging from a high tree branch. They grab the rope and hang on. How high can the rope arc upward, as measured as the vertical change in height of the person’s center of gravity? Does the length of the rope swing affect your answer? Does the mass of the person affect your answer? Ignore the mass of the rope swing. Assume no non-conservative forces, such as air resistance. Hint: at peak height, the direction of the swing motion reverses and the velocity of the swing/person system is zero.
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.
A 60 kg person, running quickly at 5.5 m/s sees a rope swing hanging from a high tree branch.
They grab the rope and hang on. How high can the rope arc upward, as measured as the vertical
change in height of the person’s center of gravity? Does the length of the rope swing affect your
answer? Does the mass of the person affect your answer? Ignore the mass of the rope swing.
Assume no non-conservative forces, such as air resistance.
Hint: at peak height, the direction of the swing motion reverses and the velocity of the
swing/person system is zero.
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