Total angular momentum of a sphere that had both a linear v and an angular v?

In summary, the net angular momentum for the given scenario can be found by vector adding the contributions from the rotational and translational motion of the soccer ball, taking into account the direction of each contribution using the right-hand rules. This can be calculated using the equations L = rmvsinθ and L=Iw, where r is the radius of the ball, m is the mass, v is the translational velocity, θ is the angle between the velocity and the radius, I is the moment of inertia, and w is the angular velocity. It is important to remember that angular momentum is a vector quantity.
  • #1
therest
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Homework Statement


Find net angular momentum for a soccer ball (moment of inertia=2/3mr^2) that's going 3.6 m/s to the right and 28.5 radians per second clockwise at the same time.
R=0.142 m
m=0.678 kg

Homework Equations


L=(perpendicular component of r)mv
L=Iw

The Attempt at a Solution


L=rmvsinθ, but L also equals I*angular velocity, a rotational analog... What if both a rotational and translational velocity exist? do I add them based on these 2 equations, or what? What about the right-hand rule?
 
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  • #2
Remember that angular momentum is a vector. You need to vector add the two contributions from the rotational and translational motion of the ball. To do this, you need to know the direction of these contributions, which you determine using the various right-hand rules.
 

1. What is total angular momentum?

Total angular momentum is a measure of the rotational motion of an object, taking into account both its linear velocity (speed in a straight line) and its angular velocity (speed around an axis). It is a vector quantity, meaning it has both magnitude and direction.

2. How is total angular momentum calculated?

The total angular momentum of a sphere can be calculated by multiplying its moment of inertia (a measure of an object's resistance to rotational motion) by its angular velocity (in radians per second) and adding the product to the product of its mass, linear velocity, and the radius of the sphere.

3. What is the significance of total angular momentum?

Total angular momentum is an important concept in physics, as it helps us understand how objects move and interact. It is conserved, meaning it remains constant unless acted upon by an external force, and is used to explain phenomena such as spinning tops, planetary orbits, and gyroscopic motion.

4. How does linear velocity affect total angular momentum?

The linear velocity of an object affects its total angular momentum by increasing or decreasing the magnitude of the total angular momentum vector. The direction of the linear velocity also plays a role in determining the direction of the total angular momentum vector.

5. Can total angular momentum be changed?

Total angular momentum can only be changed by external forces acting on the object. In the absence of external forces, the total angular momentum of a system remains constant. This is known as the law of conservation of angular momentum.

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