Rotational Motion and Moment of Inertia Questions

In summary, the conversation involved a discussion of two physics problems. The first problem dealt with a uniform rod pivoted about a horizontal, frictionless pin and the second problem involved two pulley wheels mounted on a common axle. The conversation also touched on the concept of energy and the use of equations to solve these problems. Ultimately, the conversation ended with the request for help and the promise to revisit the problems at a later time.
  • #1
hoseA
61
0
:confused:

1.)

A uniform rod of mass 0.93 kg is 17 m long.
The rod is pivoted about a horizontal, fric-
tionless pin at the end of a thin extension (of
negligible mass) a distance 17 m from the cen-
ter of mass of the rod. Initially the rod makes
an angle of 70 degrees with the horizontal. The rod
is released from rest at an angle of 70 degrees with
the horizontal.
The acceleration of gravity is 9.8 m/s^2.
Hint: The moment of inertia of the rod
about its center-of-mass is 1/12 ML^2.

What is the angular speed of the rod at
the instant the rod is in a horizontal position?
Answer in units of rad/s.

MgL/2 = .5(1/12ML^2)w^2

This works out to be:

w = sqrt(12g/L)

w = 2.630142 ?

But the answer is wrong?? why?!
---------------------------------------
2.
Two pulley wheels, or respective radii R1 =
0.34 m and R2 = 1.5 m are mounted rigidly
on a common axle and clamped together. The
combined moment of inertia of the two wheels
is I + 4.5 kg*m^2.
Mass m1 = 18 kg is attached to a cord
wrapped around the first wheel, and another
mass m2 = 5.9 kg is attached to another cord
wrapped around the second wheel.

The acceleration of gravity is 9.8 m/s^2 :
Find the angular acceleration of the system.
Take clockwise direction as positive. Answer
in units of rad/s^2.

I = .5MR^2

I1= .5(18)(.34)^2
I2= .5(5.9)(1.5)^2

I = I1 +I2 + 4.5 = 12.1779

Acceleration= [(m2gR2)-(m1gR1)]/[I+(m1r1^2)+(m2r2^2)]

= .971689752 ??

This is wrong as well, WHY??!?

Please help. All help is appreciated. :approve:
 
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  • #2
someone pls help me!... any hints appreciated. :)
 
  • #3
hoseA said:
:confused:
What is the angular speed of the rod at
the instant the rod is in a horizontal position?
Answer in units of rad/s.
MgL/2 = .5(1/12ML^2)w^2
How did you get that equation? Where have you used the fact that the rod is initially inclined at an angle of 70 degrees to the horizontal?
 
  • #4
siddharth said:
How did you get that equation? Where have you used the fact that the rod is initially inclined at an angle of 70 degrees to the horizontal?

What equation should I use then?

I found a similar pbm online that used that equation- apparently it's wrong.
 
  • #5
Well, have you thought about what concept or principle you might use to attempt this question?
 
  • #6
siddharth said:
Well, have you thought about what concept or principle you might use to attempt this question?
I know it uses Moment of Inertia in the equation... that's abt it.

I'm totally lost as to how to approach it.
 
  • #7
hoseA said:
I'm totally lost as to how to approach it.
I understand that, but it's important to think in terms of principles and concepts rather than equations. The equations will easily follow once you understand what's happening.
For instance,in this problem, what can you say about the energy of the system?
 
Last edited:
  • #8
siddharth said:
I understand that, but it's important to think in terms of principles and concepts rather than equations. The equations will easily follow once you understand what's happening.
For instance,in this problem, what can you say about the energy of the system?

Well, my brain isn't working at the moment.

I'll look at this tomorrow. Thanks for your help, nandrie, vannakam _/\_ ;).
 

What is rotational motion?

Rotational motion refers to the movement of an object around an axis or center point. This type of motion can be seen in objects such as wheels, spinning tops, and planets orbiting the sun.

What is moment of inertia?

Moment of inertia is a measurement of an object's resistance to changes in its rotational motion. It is similar to mass in linear motion, but instead relates to an object's distribution of mass around an axis.

How is moment of inertia calculated?

The moment of inertia of an object can be calculated by multiplying the mass of each particle in the object by the square of its distance from the axis of rotation, and then adding all of these values together.

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 more mass, greater distance from the axis of rotation, or a larger radius of gyration (a measure of how spread out the mass is) will have a greater moment of inertia.

Why is moment of inertia important?

Moment of inertia is important because it is a key factor in determining an object's rotational dynamics. It helps to predict how an object will behave when subjected to torque or rotational forces, and is essential in designing and understanding machines and structures that involve rotational motion.

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