Forces (moment of inertia) Question

In summary: I get it :) ,, actually I didn't focus on what he wrote ,, thanks again ,, am bothering you this day (my last day :D)In summary, the pulley has a moment of inertia of 0.5*M*R2^2. The angular acceleration of the pulley is 0.5*M*R^2. The block A and block B each have an acceleration of -0.5*M*R^2. The tensions in the strings are 0.5*M*R. The block B hits the ground at a speed of Vb = 4.0*M*R*R^2.
  • #1
Lord Dark
121
0

Homework Statement


hi everyone,, I need an explanation for this question:
A 1.0 kg block A is hanged by a light string from a pulley of mass
M = 1.0 kg. Another block B of mass 4.0 kg is attached to a mass-less rope wound around a mass-less shaft. The pulley has a radius 260.0 Rcm= and the shaft has a radius. The block B is released from rest when it is at height h = 4.0 m above the ground. 130.0 cm R=
The rotational inertia (moment of inertia) of the pulley with respect to its center of mass is.
I(com)=0.5*M*R2^2

(a) Find the angular acceleration of the pulley.
(b) Find the accelerations of the blocks.
(c) Determine the tensions in the strings.
(d) Find the speeds of the block A and block B just before the block B hits the ground.

Homework Equations


The Attempt at a Solution


Actually ,, I have the answer ,, but the problem I don't know how did he get the moment of inertia like that (in the attachment)
 

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  • #2
Lord Dark said:
Actually ,, I have the answer ,, but the problem I don't know how did he get the moment of inertia like that (in the attachment)
You have the mass of the pulley and are told the equation to use to find its moment of inertia. Maybe you can restate your question.
 
  • #3
I mean shouldn't I=I(com)+M1R1^2+M2R2^2 ??
 
  • #4
Lord Dark said:
I mean shouldn't I=I(com)+M1R1^2+M2R2^2 ??
No, those masses are not rigidly attached to the pulley. The only thing rotating here is the pulley. Treat this as three separate objects: m1, m2, and m3.
 
  • #5
then the teacher's answer is wrong ? and TbR1-TaR2=I(com)*alfa only ?? not like his answer ? (in the attachment)
 
  • #6
Lord Dark said:
then the teacher's answer is wrong ? and TbR1-TaR2=I(com)*alfa only ?? not like his answer ? (in the attachment)
What makes you think that the teacher is doing anything other than TbR1-TaR2=I(com)*alfa? (Where I is just the rotational inertia of the pulley.) That's his equation #3.

(You could lump them all together, but I would not advise it. Do it like your teacher did. Write three separate equations, then combine them.)
 
  • #7
aha ,, now I get it :) ,, actually I didn't focus on what he wrote ,, thanks again ,, am bothering you this day (my last day :D)
 

FAQ: Forces (moment of inertia) Question

What is moment of inertia?

Moment of inertia is the measure of an object's resistance to changes in its rotational motion. It is also known as rotational inertia.

How is moment of inertia different from mass?

Mass is the measure of an object's resistance to linear motion, while moment of inertia is the measure of an object's resistance to rotational motion. They are related, but moment of inertia also takes into account the distribution of mass around an axis of rotation.

How is moment of inertia calculated?

The moment of inertia is calculated by multiplying the mass of an object by the square of its distance from the axis of rotation. The equation is I = mr², where I is the moment of inertia, m is the mass, and r is the distance from the axis of rotation.

What factors affect the moment of inertia of an object?

The moment of inertia is affected by the mass of the object, the shape of the object, and the distance of the mass from the axis of rotation. Objects with more mass, spread out over a larger distance from the axis of rotation, have a higher moment of inertia.

How does moment of inertia impact rotational motion?

The moment of inertia determines how easily an object can be rotated. Objects with a higher moment of inertia require more force to rotate, while objects with a lower moment of inertia can be rotated with less force. This is why objects with a lower moment of inertia, such as a figure skater pulling in their arms, can rotate faster than objects with a higher moment of inertia, such as a spinning top.

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