Rotational Angular Momentum of a Bowling Ball

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SUMMARY

The discussion focuses on calculating the rotational and translational angular momentum of a 7 kg bowling ball with a radius of 0.13 m, rolling at three revolutions per second. The rotational angular momentum is derived using the formula L = Iω, where I is the moment of inertia (2/5 * m * r²) and ω is the angular velocity (6π rad/s). The translational angular momentum is defined as the angular momentum about the center of mass plus the contribution from the motion of the center of mass itself. The conversation highlights the distinction between these two types of angular momentum.

PREREQUISITES
  • Understanding of angular momentum concepts
  • Familiarity with the moment of inertia calculation
  • Knowledge of angular velocity and its units
  • Basic principles of rotational dynamics
NEXT STEPS
  • Calculate the moment of inertia for different shapes using the formula I = 2/5 * m * r²
  • Explore the relationship between linear and angular momentum
  • Learn about the conservation of angular momentum in various systems
  • Investigate the effects of rolling motion on angular momentum
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KatlynEdwards
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Homework Statement


A 7 kg bowling ball whose radius is 0.13 m is rolling directly toward you turning three times per second. What are the magnitude and direction of its rotational angular momentum about you? What is its translational angular momentum about you?


Homework Equations


L = r x p = r x (m*v)
L = I\omega
L of a moving object = Lcm + Lrot

The Attempt at a Solution


So I was thinking the rotational angular momentum is L = i\omega which is 2/5*m*r2\omega
Which would be (2/5)*7*(0.13)2*(6*pi / 1 sec)
But I don't know how to get the translational angular momentum.
 
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Hi Katlyn! :smile:

(have an omega: ω and a pi: π :wink:)
KatlynEdwards said:
A 7 kg bowling ball whose radius is 0.13 m is rolling directly toward you turning three times per second. What are the magnitude and direction of its rotational angular momentum about you? What is its translational angular momentum about you?

But I don't know how to get the translational angular momentum.

That's a rather weird question.

I think what they mean is that when you measure the angular momentum of a body about an axis, it's the angular momentum about a parallel axis through the centre of mass, plus the angular momentum of the whole mass as if it were at the centre of mass, and moving with the same velocity as the centre of mass …

I think they're calling the second one translational angular momentum. :smile:

(Though then they must be calling the first one "the rotational angular momentum about you" when it quite clearly isn't about you :confused:)
 

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