Angular momentum of a falling ball

North.In summary, the conversation discusses the calculation of angular momentum and its direction. The calculation is found to be correct and the direction is determined to be clockwise, specifically towards the North direction.
  • #1
ac7597
126
6
Homework Statement
Polly climbs to the top floor of her dorm, a height H=90 meters above the ground. She holds a ball of mass m=2 kg in her hand. She sticks her arm out a window facing East, so that the ball is d=0.77 meters away from the window. Polly then drops the ball.

Ignore air resistance

What is the angular momentum of the ball measured from the window at a time t1=0.7 seconds after Polly drops the ball? Provide both a magnitude and direction.

What is the angular momentum of the ball measured from the window at a time t2=1.8 seconds after Polly drops the ball? Provide both a magnitude and direction.

What is the angular momentum of the ball measured from the window at a time t3=2.4 seconds after Polly drops the ball? Provide both a magnitude and direction.
Relevant Equations
angular momentum(L) = (radius) * (mass*velocity)
(L) = (radius) * (mass*velocity)
velocity= 0+ (9.8m/s^2) (0.7s) = 6.86m/s
(L) = (0.77m) * (2kg*6.86m/s)= 1.05 kg*m^2/s
angular momentum points towards Polly
 
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  • #3
is the calculation correct?
 
  • #4
ac7597 said:
is the calculation correct?
Looks right. What do you get for direction now?
 
  • #5
direction is perpendicular to the velocity of the body. Thus it is a horizontal direction: left
 
  • #6
ac7597 said:
direction is perpendicular to the velocity of the body. Thus it is a horizontal direction: left
From Polly's view, yes.
 
  • #7
Does it mean the direction is clockwise?
Apparently left, right, west, east is not correct.
 
  • #8
ac7597 said:
Does it mean the direction is clockwise?
Apparently left, right, west, east is not correct.
She is facing East, so which direction is left?
 
  • #9
North
 
  • #10
ac7597 said:
North
Right
 

1. What is angular momentum?

Angular momentum is a measure of how much rotational motion an object has. It is calculated by multiplying an object's moment of inertia (a measure of its resistance to rotation) by its angular velocity (the rate at which it is rotating).

2. How is angular momentum related to a falling ball?

As a ball falls, it gains rotational motion due to its asymmetrical shape and air resistance. This causes its angular momentum to increase as it falls.

3. What factors affect the angular momentum of a falling ball?

The angular momentum of a falling ball is affected by its mass, shape, and the air resistance it experiences as it falls. The larger the mass and the more asymmetrical the shape, the greater the angular momentum will be.

4. Does the height of the fall affect the angular momentum of a ball?

Yes, the height of the fall does affect the angular momentum of a ball. The higher the fall, the more time the ball has to gain rotational motion and therefore, the greater its angular momentum will be when it reaches the ground.

5. How can the angular momentum of a falling ball be calculated?

The angular momentum of a falling ball can be calculated using the formula L = Iω, where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity. The values for these variables can be determined by measuring the mass, shape, and rotational speed of the ball.

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