Calculating Linear and Rotational Motion

In summary, the ball has a momentum before the collision of (mvxL/I) and after the collision it has the momentum of (mvxL/I). The pole has a velocity before and after the collision.
  • #1
Knightycloud
86
0

Homework Statement


In this given pole, mass is "M" and length is "L" and it is on a frictionless surface as the picture describes. "G" is the center of gravity and "I" is the inertia.
A ball with a mass of "m" comes as the picture and hits the pole with a velocity of "v" and turns the opposite side and leaves at the same velocity. Then the pole moves under both rotational and linear motions.


Homework Equations


(a)
i. Write an equation for the momentum of the ball before the collision.
ii. Considering only the linear motion of the pole, write an equation for the velocity of the pole "V".

(b) Now consider the rotational motion.
i. If the ball hits x distance from point "G", write an equation for the angular momentum of the ball around point "G".
ii. Write an equation for the angular velocity of the pole around point "G"



The Attempt at a Solution


(a)
i. P = mv
ii. → mv + M0 = -mv + MV
∴ V = [itex]\frac{2mv}{M}[/itex]

(b)
i. L = mvx
ii. → mvx + 0 = -mvx + Iω
∴ ω = [itex]\frac{2mvx}{I}[/itex]
 

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  • #2
Hi Knightycloud! :smile:

(btw, we'd say "opposite way" rather than "opposite side" :wink:)

Yes, that's fine …

what is worrying you about that?​
 
  • #3
Yeah! :D
well did I get that b part correct?
 
  • #4
yes :smile:
 
  • #5
Oh, So did i get that angular velocity correct?
then the question asks at a certain value of x (lets say it's y) the point A becomes still. How to calculate that value Y?
 
  • #6
let's see :rolleyes: … A is at distance -L/2 from the centre

ok, from (a) and (b), what is the initial velocity of A? :smile:
 
  • #7
Velocity of point A is mvxL/I
and thank you, I found the solution to the rest of the question :D I've been a bit lossing my self confidence! You know even if I had the answer, I believed it wrong!

That Y distance is = 2I/ML by the way!
Thanks Tim!
 

What is linear motion?

Linear motion is the movement of an object in a straight line, where the distance traveled is the same as the displacement.

What is rotational motion?

Rotational motion is the movement of an object around an axis or point, where the distance traveled is not the same as the displacement.

What is the difference between linear and rotational motion?

The main difference between linear and rotational motion is the type of path that the object follows. In linear motion, the object moves along a straight line, while in rotational motion, the object moves in a circular path around an axis or point.

What are some examples of linear and rotational motion?

Examples of linear motion include the movement of a car along a road, a person walking in a straight line, or a ball rolling down a hill. Examples of rotational motion include the rotation of a spinning top, the movement of a Ferris wheel, or the rotation of the Earth around its axis.

How does mass and force affect linear and rotational motion?

In linear motion, mass and force affect the acceleration and velocity of an object. In rotational motion, mass and force affect the angular acceleration and angular velocity of an object. The greater the mass or force, the greater the effect on the motion of the object in both linear and rotational cases.

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