Rotational problem another time (this time not the center of mass)

In summary: And that's vtop.In summary, the problem involves finding the linear speed, vtop, of a point on the top of a chimney that cracks and topples, given its length and mass. The chimney is assumed to behave like a thin rod, experience only gravity, and tilt at the bottom without moving left or right. Using conservation of energy and the equation v=ωr, the solution is found to be v = √(3g/L) * L, with ω being the same as the one found in a previous problem.
  • #1
NasuSama
326
3

Homework Statement



A chimney (length L = 82.6 m, mass M = 2280 kg) cracks at the base, and topples. Assume:
- the chimney behaves like a thin rod, and it does not break apart as it falls
- only gravity (no friction) acts on the chimney as if falls
- the bottom of the chimney tilts but does not move left or right

Find vtop, the linear speed of a point on the top of the chimney just as it hits the ground.

Homework Equations



→Conservation of energy
→KE = ½Iω²?
→v = ωr?

The Attempt at a Solution



What if I tried this method?

mgL = ½ * 1/3 * mL² * ω²
ω = √(6g/L)

Then...

v = √(6g/L) * L

But the whole answer is wrong.
 
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  • #2
  • #3
NasuSama said:
What if I tried this method?

mgL = ½ * 1/3 * mL² * ω²
What's the change in PE for the chimney as it falls? (Nothing has changed from your earlier problem except the point you are finding the speed of.)

And since this problem is an offshoot of your other one, why start a separate thread? You've already done the hard work in your other thread. You've found ω.
 
  • #4
Doc Al said:
What's the change in PE for the chimney as it falls? (Nothing has changed from your earlier problem except the point you are finding the speed of.)

And since this problem is an offshoot of your other one, why start a separate thread? You've already done the hard work in your other thread. You've found ω.

Why is it that there is the same speed of the chimney on the top as the center of mass?
 
  • #5
I mean why is it that there is the same angular speed?
 
  • #6
Sorry for another post.

Then, using the same ω instead of different ω, we have...

v = ωr
= √(3g/L) * L

Instead of L/2, we have L since we want to find the speed of the top of the chimney.

Sorry for another thread. I thought this problem would be totally different from the previous one.
 
  • #7
NasuSama said:
I mean why is it that there is the same angular speed?
Did anything change? It's the same chimney falling in the same manner. Why would the angular speed be different?
 
  • #8
Doc Al said:
Did anything change? It's the same chimney falling in the same manner. Why would the angular speed be different?

Nvm. I was stumped and unclear of the situation here. Now, I should get it.

It's just v = √(3g/L) * L [with same ω]
 
  • #9
NasuSama said:
Then, using the same ω instead of different ω, we have...

v = ωr
= √(3g/L) * L

Instead of L/2, we have L since we want to find the speed of the top of the chimney.
Good.
 

Related to Rotational problem another time (this time not the center of mass)

1. What is the difference between rotational motion and translational motion?

In rotational motion, an object rotates around an axis, while in translational motion, the object moves in a straight line. Rotational motion involves circular or angular motion, while translational motion involves linear motion.

2. How do you calculate the moment of inertia for an object?

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

3. How does the distribution of mass affect an object's rotational motion?

The distribution of mass affects an object's rotational motion by changing its moment of inertia. Objects with more mass concentrated further from the axis of rotation have a larger moment of inertia and therefore require more torque to rotate at the same speed.

4. How does angular velocity differ from linear velocity?

Angular velocity is the rate at which an object rotates around an axis, while linear velocity is the rate at which an object travels in a straight line. Angular velocity is measured in radians per second while linear velocity is measured in meters per second.

5. How does torque relate to rotational motion?

Torque is the force that causes an object to rotate around an axis. The greater the torque, the greater the acceleration of the object's rotational motion. Torque is calculated by multiplying the force applied to an object by the distance from the axis of rotation.

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