Rotational mechanics and Angular Momentum- help needed to check over work

In summary, the conversation is about a student struggling with a series of physics problems and seeking help to understand where they went wrong. They discuss problems involving rotational mechanics and the equations needed to solve them. The student provides their attempted solutions for each problem and mentions that they have received help from a forum but still did not get the correct answers. The student is seeking further assistance in order to complete their homework, which is due soon.
  • #1
ultrapowerpie
58
0
Please note, this is a series of problems, with a series of answers. I believe that I understand how to do the problems, but for some reason, my answer is wrong, and I can think of no reason why.

Homework Statement


Problem 1: http://img355.imageshack.us/my.php?image=physics1jw9.png

i) I need to find the speed of the mass as it passes point B in m/s

ii) I need to find the Tension of the string (Which I am sure I can do, but without a correct answer for part i, I'm not going to attempt yet)

Problem 2: http://img186.imageshack.us/my.php?image=physics2pt6.png

Problem 3: http://img355.imageshack.us/my.php?image=physics3el2.png
(Note, the word that is cut off is longitudinal. I had to copy and paste parts of it into one picture, sorry it's a little shoddy <.<)

Homework Equations


All the lovely rotational mechanics equations, and their linear counterparts


The Attempt at a Solution



Problem 1
i) Ok, I did not take into account the spoke on teh wheel whatsoever, since the mass of inertia was given to me, and the spokes of the wheel did not seem to have their own mass. Not sure if this would effect the problem.

T=I(angular a)
Angular acceleration = Torque/I

Torque= 46 KG * 9.8 m/s^2 * 3m = 1352.4
I= 3/4* 23 KG * 3^2 = 155.25
Ang A= 8.7111

a = (Ang A)*r

a= 8.711 * 3 = 26.133

Plugging this acceleration into the classic Xf= Xi + Vi +(at^2)*2 (assuming Vi and Xi are 0)
I get t=2.106

Then, using the Vf= Vi +at
I get Vf= 55.05

This answer is wrong though, not sure where I screwed up




Problem 2
This one seemed simple enough, just a basic torque= I * ang a

Ang a = T/I

I=(1/12)*(2.7)*(3^2)= 2.025

T= rxF
F= M*G= 9.8*2.7= 26.46
r= 3cos(43)=2.045
T= 54.137

Ang a= 26.734

It wants it in Radians/sec^2. Is it bad that I was using degrees for the cos?


Problem 3
I searched on google, and did come across this thread: https://www.physicsforums.com/showthread.php?t=17605

However, upon trying the forumulas given there, I still got it wrong. Using the formula ShawnD had at the end of his post, I got the wrong answer.

m= IW/rV

I= 2950
W=2 rev/min= .2094... rad/sec
r=2.9
V=755
I got M to be .282 kg

I then divided by .012 kg, and got that time = 21.87 s

This answer is also wrong, not sure what happened.

Thank you in advance for looking over this work.
 
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  • #2
Slight bump, sorry, but homework's due by Thursday Night. >.>
 
  • #3


Dear student,

It is great that you are seeking help to check over your work. It shows that you are taking your studies seriously and want to make sure you are understanding the material correctly.

For problem 1, it seems like you have the right approach, but your calculations may have some errors. Here are some suggestions for you to check:

- Make sure you are using the correct units for all the quantities. For example, the torque should be in Newton-meters (N*m) and the moment of inertia should be in kg*m^2.
- Double check your calculation for moment of inertia. The formula you used, I = 3/4 * 23 kg * 3^2, seems to be for a solid disk, but the problem gives the moment of inertia for a hoop. The correct formula for a hoop is I = MR^2, where M is the mass and R is the radius.
- When calculating angular acceleration, make sure you are using the correct value for moment of inertia. In your calculation, you used the moment of inertia for the disk instead of the hoop.
- Lastly, when using the kinematic equations for rotational motion, make sure you are using the correct equation for the situation. In this problem, the mass is moving in a circular motion, so you should use the equation Vf = Vi + a*t. The equation Vf = Vi + a*t^2/2 is used for linear motion.

For problem 2, you are correct in using degrees for the cosine function. However, you should also convert the angle to radians when calculating the torque, as the formula for torque is T = rFsin(theta), where theta is in radians. So the correct calculation for torque should be T = (3*cos(43*pi/180)) * (26.46*sin(43*pi/180)) = 27.06 N*m. Then, use this value for torque in your calculation for angular acceleration.

For problem 3, it seems like you have the right formula, but there may be some errors in your calculation. Here are some suggestions to check:

- Again, make sure you are using the correct units for all the quantities. The moment of inertia should be in kg*m^2 and the angular velocity should be in radians per second.
- Double check your calculation for moment of inertia. The formula you used, I = 2950, does not seem to be correct. The moment of inertia for
 
1.

What is rotational mechanics and angular momentum?

Rotational mechanics is the branch of physics that deals with the motion of objects that rotate around an axis. Angular momentum is a measure of an object's rotational motion, calculated by multiplying its moment of inertia by its angular velocity.

2.

How is angular momentum conserved in rotational systems?

Angular momentum is conserved in rotational systems because, in the absence of an external torque, the total angular momentum of a system remains constant. This means that if one part of the system gains angular momentum, another part must lose an equal amount in the opposite direction.

3.

What is the relationship between torque and angular acceleration?

Torque is the rotational equivalent of force and is responsible for causing angular acceleration. The relationship between torque and angular acceleration is described by the equation τ = Iα, where τ is torque, I is moment of inertia, and α is angular acceleration.

4.

How do you calculate moment of inertia?

Moment of inertia is calculated by summing the products of each particle's mass and its distance from the axis of rotation squared. This can be simplified to I = mr^2 for a single point mass, or by using the parallel axes theorem for more complex objects.

5.

What are some real-world applications of rotational mechanics and angular momentum?

Rotational mechanics and angular momentum have various applications in everyday life, including the motion of objects such as wheels, tops, and planets. They are also important in engineering fields such as robotics, where understanding rotational motion is necessary for designing efficient and stable systems.

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