Moment of Interia. Help please.

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In summary, the hanging mass takes 6.1 seconds to fall 31.5 cm and the total moment of inertia of the masses plus rod and shaft is 6.286E-03 kg m^2. This can be calculated using the equation I=2MR^2+Io, where M is the mass of the hanging mass, R is the distance from the point of rotation, and Io is the moment of inertia of the support rod and shaft.
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jago-k1
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Homework Statement


How long does it take for the hanging mass to fall the same distance 31.5 cm?
I don't know how to solve for T with everything I have. Help please.

Homework Equations



mgh=(1/2)I(2h/tr)2 + (1/2)m(2h/t)2

The Attempt at a Solution



Okay, previous questions are[All correct]
1.
Two masses of 150. g are suspended from a massless rod at a distance of 9.0 cm from the center. What is the moment of inertial of the two-mass system about the center of the rod?

I=m1*R^2
since they are two masses that weigh the same
I= 2(.15kg)(.09m)^2=2.43E-03 Correct


2.
If the masses rotate with an angular velocity of 2.45 rad/s, what is the rotational kinetic energy of the system?

KEr=(1/2)Iw^2 = (2.43E-03 )(2.45 rad/s)^2 = 7.29E-03 J Correct


3.
Consider the setup shown in the lab manual but with the large masses removed from the support rod. If the hanging mass is 100. g and drops a distance 31.5 cm in a time of 6.1 s, what is the moment of inertia of the support rod and shaft? The radius of the shaft is 0.50 cm.

I=mr^2(gt^2/2h - 1) = 1.446E-03 kg m^2 Correct


4.
Now two masses each of 200 g are placed on the rod at a distance of 11.0 cm from the point of rotation. What is the TOTAL moment of inertia of the masses plus rod and shaft?
Yes, Computer gets: 6.286E-03 kg m^2

I=2MR^2+Io is what you get from #3
I=2(.2kg)(.11m)^2 + Io = 6.286E-03 kg m^2 Correct
 
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  • #2
BUMP if anyone can help out.
 
  • #3



First, it's great that you are actively trying to solve your homework problems. As a scientist, it's important to approach problems with curiosity and a willingness to try new things.

To solve for the time it takes for the hanging mass to fall a distance of 31.5 cm, we can use the equation for gravitational potential energy: mgh = (1/2)I(2h/t)^2, where m is the mass of the hanging object, g is the acceleration due to gravity, h is the distance fallen, and t is the time it takes to fall that distance.

Since we know the values for m, g, and h, we can rearrange the equation to solve for t: t = √(2h/mg). Plugging in the values, t = √(2*0.315 m)/(0.1 kg*9.8 m/s^2) ≈ 0.8 seconds.

I hope this helps! Remember to always show your work and double check your units to ensure you get the correct answer. Keep up the good work!
 

1. What is moment of inertia?

Moment of inertia is a physical property of an object that describes its resistance to changes in rotational motion. It is a measure of an object's distribution of mass around an axis.

2. How is moment of inertia calculated?

Moment of inertia can be calculated by multiplying the mass of an object by the square of its distance from the axis of rotation. This can be represented by the formula I = mr^2, where I is the moment of inertia, m is the mass, and r is the distance from the axis of rotation.

3. What factors affect moment of inertia?

The moment of inertia of an object is affected by its mass, shape, and distribution of mass. Objects with larger mass or a greater distance from the axis of rotation will have a larger moment of inertia.

4. How is moment of inertia used in real life?

Moment of inertia is an important concept in physics and engineering, and is used to analyze the behavior of rotating objects. It is also used in the design of various machines and structures, such as bicycles, cars, and buildings.

5. Why is moment of inertia important?

Moment of inertia is important because it helps us understand and predict the rotational motion of objects. It is also important in engineering and design, as it allows us to determine the amount of force needed to accelerate or decelerate a rotating object.

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