Rotating Bracelet. Enrico owns a circular bracelet of mass m = 23 g and diameter d0 = 6.9 cm, which is made of n identical small beads each connected with massless springs of spring constant nk where k = 0.5 N/m. (a) Through some unknown superpower, Enrico manages to make this bracelet levitate and spin horizontally (i.e. axis of rotation is vertical) with an initial angular velocity of ω = 10 rad/s without touching it. This causes the bracelet to lengthen, increasing its diameter. Despite this, Enrico forces the bracelet to maintain a constant angular velocity. Enrico observes that the diameter of this bracelet initially varies, but after a long time, it settles at a constant value d. For large n, what value does d approach? (b) Enrico repeats what he did previously, but this time, the bracelet no longer maintains a constant angular velocity. Again, Enrico observes that the diameter of this bracelet initially varies, but after a long time, it settles at a constant value d. For large n, what value does d approach?
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.
Rotating Bracelet. Enrico owns a circular bracelet of mass m = 23 g and diameter d0 = 6.9 cm, which is made of n identical small beads each connected with massless springs of spring constant nk where k = 0.5 N/m.
(a) Through some unknown superpower, Enrico manages to make this bracelet levitate and spin horizontally (i.e. axis of rotation is vertical) with an initial
(b) Enrico repeats what he did previously, but this time, the bracelet no longer maintains a constant angular velocity. Again, Enrico observes that the diameter of this bracelet initially varies, but after a long time, it settles at a constant value d. For large n, what value does d approach?
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