Comparing Inertia of Disk, Hoop, & Sphere

  • Thread starter maverick19
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In summary, the sphere would be the object with the smallest moment of inertia about the axis, the hoop would experience the largest net torque, the sphere would undergo the smallest angular acceleration, the sphere would have the largest angular speed after 5 seconds, the sphere would have the largest amount of string unraveled in 5 seconds, and the sphere would undergo the most rotations in 5 seconds. As for the object with the smallest KE(rotational) after 5 seconds, it can be determined by solving for the total energy or using the information from the previous answers.
  • #1
maverick19
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A uniform disk(I=.5mr^2), hoop(I=mr^2), and sphere(I=.4mr^2), all with the same mass and radius, can freely rotate about an axis through the center of mass (CM) of each. A massless string sis wrapped around each item. The string is used to apply a constant and equal tangential force to each object. Enter D, H, S, or none or the same for the statements.

1) The one with the smallest moment of inertia about the axis
2) The object experiencing the largest net torque
3) The object undergoing the smallest angular acceleration
4) The object with the largest angular speed after an elapsed time of 5 seconds
5) The object for which the largest amount of string has unraveled in 5 seconds
6) The object with the smallest KE(rotational) after 5 seconds
7) The object that undergoes the most rotations in 5 seconds

I want to make sure I understand concept of how inertia relates so these are my answers:
1) Sphere, object with the smallest multiplier
2) Hoop, torque=I x angular accelerations so the object with the largest multiplier in the inertia
3) Sphere, mgh=.5mv^2 + .5Iw^2. .5Iw^2=.5(.5 or 1 or .4)mv^2. So if you solve for the velocity you would divide the other side of the equation by .5, 1, or .4 and dividing by .4 would give you the greatest velocity which means the a bigger s(arc length) which would give you a bigger angular acceleration
4) Sphere, same mentality as above
5) Sphere, same mentality as above
6) I'm not sure about this ne
7) Sphere


I am really not sure if I understand this stuff so please help me and if I got any wrong and explanation of why would be greatly appreciated because I want to understand why.


Thanks!
 
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  • #2
2) Hoop, torque=I x angular accelerations so the object with the largest multiplier in the inertia
Check which values are the same in the 3 setups. It is not the angular acceleration.

3) Sphere, mgh=.5mv^2 + .5Iw^2. .5Iw^2=.5(.5 or 1 or .4)mv^2.
Which h, which v? What are you calculating there at all?

4) Sphere, same mentality as above
While this is the right answer here, it is inconsistent with your (wrong) 3. Small angular acceleration corresponds to a smaller angular velocity after 5 seconds.

6 can be solved with a correct 3 and the formula for the total energy. Alternatively, you can use 5 to answer this.

7 follows from 4 or 5.
 

What is inertia?

Inertia is the tendency of an object to resist changes in its motion. It is directly related to an object's mass, with more massive objects having greater inertia.

How does the inertia of a disk compare to that of a hoop and a sphere?

The inertia of a disk, hoop, and sphere all depend on their mass and distribution of mass. In general, a disk and hoop have similar inertia, while a sphere has a greater inertia due to its mass being more evenly distributed.

Why is it important to compare the inertia of different objects?

Comparing the inertia of different objects can help us understand how different factors, such as mass and distribution of mass, affect an object's resistance to changes in motion. This information can be useful in engineering and designing structures and machines.

How can the inertia of an object be measured?

The inertia of an object can be measured by performing experiments that involve changing the object's motion and measuring the force required to do so. The greater the force needed to change an object's motion, the greater its inertia.

What real-life applications are there for understanding the inertia of different objects?

Understanding the inertia of different objects is crucial in many real-life applications, such as designing cars and other vehicles, creating sports equipment, and even analyzing the movements of celestial bodies in space. It also helps us understand the behavior of objects in everyday situations, such as when riding a bike or playing with a ball.

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