For our dynamic measurement of the moment of inertia, we will use a vertically-mounted turntable that has a hub attached at its center, which has three grooves of different radius, around which one can wind a string. A mass hanging from the free end of the string provides tension, which exerts a torque on the turntable, thus causing it to rotate. By measuring the time it takes the mass to fall from its initial height to the table top (or some reference line just above it), we can find aa, its (linear) acceleration. From this we can calculate αα, the angular acceleration of the turntable. From the weight of the mass, and its linear acceleration, we can find T, the tension in the string. Once we know all these things, we can calculate the torque, ττ, and from τ=Iατ=Iα find I, the moment of inertia of our turntable platter. Assumptions made in this experiment: - Turntable disk mass/density was distributed evenly (this is not the case, it is actually concentrated in center) - Assumed that there was a central axis of rotation on the disk (this might not be the case, as central axis could have been offset accidentally). In what way could these assumptions cause a discrepancy between the accepted and experimental values obtained for the moment of inertia?
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.
Looking for guidance to question based on characteristics/assumptions of experiment:
Experiment background:
For our dynamic measurement of the moment of inertia, we will use a vertically-mounted turntable that has a hub attached at its center, which has three grooves of different radius, around which one can wind a string. A mass hanging from the free end of the string provides tension, which exerts a torque on the turntable, thus causing it to rotate. By measuring the time it takes the mass to fall from its initial height to the table top (or some reference line just above it), we can find aa, its (linear) acceleration. From this we can calculate αα, the
Assumptions made in this experiment:
- Turntable disk mass/density was distributed evenly (this is not the case, it is actually concentrated in center)
- Assumed that there was a central axis of rotation on the disk (this might not be the case, as central axis could have been offset accidentally).
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In what way could these assumptions cause a discrepancy between the accepted and experimental values obtained for the moment of inertia?
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