Angular momentum/angular velocity.

In summary, we have a solid cylinder rotating about a vertical axis with a given mass and radius. A piece of putty is dropped onto the cylinder and sticks, causing the moment of inertia to change. Using the conservation of angular momentum, we can set up an equation to solve for the final angular velocity of the system. The parallel axis theorem is used to account for the change in moment of inertia.
  • #1
the whizz
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0

Homework Statement



1.A solid, vertical cylinder of mass 10.0 kg and radius 1.00 m rotates with an angular speed of 7.00 rad/s about a fixed vertical axis through its center. A .250 kg piece of putty is dropped vertically onto the cylinder at a point 0.900 m from the center of ration and sticks to the cylinder. Determine the final angular speed of the system.


Homework Equations



Lbefore=Lafter
L=Iw

The Attempt at a Solution



the angular momentum is L and the angular velocity is what i am looking for that is w.
I believe you can say that IoWo should = IW

I am unsure what you are to do with the mass of the putty and the center of radian issue.

I believe you need to set up taht W = (Io/I)wo

Io = MR^2?
 
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  • #2
[tex] I_{o}\times \omega_{o}=I_{f}\times \omega_{f} [/tex]

We know [tex] I_{o}= \frac{1}{2}MR^2 [/tex] plus we know wf

[tex] I_{f}=\frac{1}{2}MR^2+mr^2 [/tex]
Note: the [tex] I_{f} [/tex] changes, the parallel axis theorm is used.

only [tex] \omega_f [/tex] left that's unknown.
 
  • #3




I would like to clarify some of the information provided and provide a possible solution to the problem.

First, angular momentum (L) is a property of a rotating object and is defined as the product of its moment of inertia (I) and its angular velocity (w). It is a vector quantity, meaning it has both magnitude and direction.

In this problem, we are given a solid, vertical cylinder with a mass of 10.0 kg and a radius of 1.00 m. It is rotating with an angular speed of 7.00 rad/s about a fixed vertical axis through its center. We are also given a piece of putty with a mass of 0.250 kg that is dropped vertically onto the cylinder at a point 0.900 m from the center of rotation and sticks to the cylinder.

To determine the final angular speed of the system, we need to use the conservation of angular momentum, which states that the total angular momentum before and after an event remains constant, as long as there is no external torque acting on the system.

Before the putty is dropped, the angular momentum of the system is given by Lbefore = Iwo, where I is the moment of inertia of the cylinder and wo is the initial angular velocity. The moment of inertia of a solid cylinder is given by I = MR^2, where M is the mass of the cylinder and R is its radius. Therefore, Lbefore = (10.0 kg)(1.00 m)^2(7.00 rad/s) = 70.0 kg m^2/s.

After the putty is dropped and sticks to the cylinder, the moment of inertia of the system changes. We can calculate the new moment of inertia, I', by adding the moment of inertia of the cylinder with the moment of inertia of the putty, which can be approximated as a point mass at a distance of 0.900 m from the center of rotation. Therefore, I' = (10.0 kg)(1.00 m)^2 + (0.250 kg)(0.900 m)^2 = 10.81 kg m^2.

Since the total angular momentum must remain constant, we can set Lbefore = Lafter and solve for the final angular velocity, wf. Therefore, (10.81 kg m^2)(wf) = (70.0 kg m^2/s), and solving for wf gives us wf =
 

What is angular momentum?

Angular momentum is a measure of an object's rotational motion. It is a vector quantity that takes into account an object's mass, size, shape, and rate of rotation.

How is angular momentum different from linear momentum?

Linear momentum refers to an object's motion in a straight line, while angular momentum refers to an object's motion around an axis or point. Linear momentum is a product of an object's mass and velocity, while angular momentum is a product of an object's moment of inertia and angular velocity.

What is angular velocity?

Angular velocity is the rate at which an object rotates around an axis or point. It is a vector quantity that takes into account an object's rotational speed and direction.

How is angular velocity calculated?

Angular velocity is calculated by dividing the change in an object's angular displacement by the change in time. It is measured in radians per second.

What factors affect an object's angular momentum?

The factors that affect an object's angular momentum include its mass, moment of inertia, and angular velocity. Additionally, external forces, such as torque, can also affect an object's angular momentum.

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