1. a) What would happen to the graph\'s slope and y-intercept if a 0.03kg disk w
ID: 1474387 • Letter: 1
Question
1. a) What would happen to the graph's slope and y-intercept if a 0.03kg disk was used instead of a 0.5kg disk (moment of inertia)?
b) What happens to the acceleration as the moment of inertia increases?
c) Does a disk with a diameter of 5cm have a larger moment of inertia than a disk with a 10cm diameter? The masses are the same.
d) What is the physical significance of Io and what does it represent?
e) When a figure skater does a spin, and they pull their arms in, the spin rate increases. why is this?
Explanation / Answer
a.)y intercept will increase and
and at constatnt radius the slope of the graph increases.
b.)as the moment of inertia increases the acceleration decreases because a moment of inertia is quantity expressing a body's tendency to resist angular acceleration, which is the sum of the products of the mass of each particle in the body with the square of its distance from the axis of rotation.
c.)No, moment of inertia is directly proportional to square of radius so as radius icreases moment of inertia increases.
d.) The moment of inertia of an object about a given axis describes how difficult it is to change its angular motion about that axis. For example, consider two discs of the same mass, one large and one small in radius. Assuming that there is uniform thickness and mass distribution, the larger radius disc requires more effort to accelerate it (i.e. change it angular motion) because its mass is effectively distributed further from its axis of rotation. Conversely, the smaller radius disc takes less effort to accelerate it because its mass is distributed closer to its axis of rotation. Quantitatively, the larger disc has a larger moment of inertia, whereas the smaller disc has a smaller moment of inertia.
The moment of inertia has two forms, a scalar form I (used when the axis of rotation mathbf{hat{n}} is known) and a more general tensor form mathbf{I} that does not require knowing the axis of rotation. The scalar moment of inertia I is often called simply the "moment of inertia".
e.)spin rate increases,
as angular momentum remains conserve so as I decreases angular velocity will increase.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.