Conservation of Angular momentum question.

In summary, the conversation discusses the use of conservation of angular momentum to determine the final angular velocity and change in kinetic energy of a system after a collision between an object and a cylinder. The attempt at a solution involves using the equation L=IW and the given values of mass and velocity to solve for the final angular velocity. However, it is important to note that linear momentum and angular momentum are not the same thing and the equation should be adjusted accordingly.
  • #1
greg_jones20
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0

Homework Statement



An object of mass 25gm and horizontal velocity of 125 cm/s strikes and sticks to the top of a cylinder of mass 333gm and radius 25cm at rest.
a) Use conservation of angular momentum to determine the final angular velocity of the combination after the collision.
b) What is the change in the kinetic energy of the system?

Homework Equations


Angular Momentum(L) = IW, where I is moment of inertia and W is angular velocity. and
Momentum(P) = mass(m)*velocity(v),

The Attempt at a Solution



Lo = Lf
m1*Vo + I*Wo = If*Wf [here, Wo=0, m1=25gm, If=1/2(m1+m2)R^2, Wf = Vf/R]
(.025kg)(1.25m/s) + 0 = [1/2(.025kg+.333kg)(.25m)^2]Vf
Tried to solve for Vf from above eqn. but couldn't get the units to work out correctly.
 
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  • #2
Linear momentum p and angular momentum L are not the same thing. You need to use the angular momentum of the first object, not its linear momentum, in your conservation of angular momentum equation.
 

What is conservation of angular momentum?

Conservation of angular momentum is a fundamental law of physics that states that the total angular momentum of a closed system remains constant over time, unless an external torque is applied.

Why is conservation of angular momentum important?

Conservation of angular momentum is important because it helps us understand the behavior of rotating objects and systems, from tiny particles to large celestial bodies. It also plays a crucial role in various fields such as mechanics, astronomy, and engineering.

How is angular momentum conserved?

Angular momentum is conserved through the principle of inertia, which states that an object will continue to rotate at a constant speed and direction unless acted upon by an external torque. This means that any change in the rotational motion of a system must be balanced by an equal and opposite change in another part of the system.

What is the relationship between angular momentum and torque?

Torque is the measure of the force that causes an object to rotate, while angular momentum is the measure of an object's rotational motion. The two are related through the equation L = Iω, where L is angular momentum, I is the moment of inertia, and ω is angular velocity. This relationship shows that changes in torque can affect the angular momentum of a system.

Can angular momentum be created or destroyed?

No, angular momentum cannot be created or destroyed. It can only be transferred between different parts of a system or between a system and its surroundings. This is known as the law of conservation of angular momentum.

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