Calculating Final Angular Speed of Rotating Table

In summary, the problem involves a 40kg duck and a 100kg rotating circular table with a rotational inertia of 250kg*m^2. The duck moves from a radius of 2.5m to 1.5m, and the initial angular speed of the table is 2.0rad/sec. Using conservation of angular momentum, the final angular speed of the table can be found by calculating the total inertia of the system and applying the conservation law.
  • #1
gamer1319
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0

Homework Statement


a 40kg duck walks from the outside to the inside of a rotating circular table of mass 100kg. if the rotational intertia of the table is 250kg*m^2 and the duck moves from a radius of 2.5m to 1.5m, find the final angular speed of the table if it rotates at 2.0rad/sec at the moment the duck begins to move.

THANKS! I'm studying for a test and i can't do this question



Homework Equations





The Attempt at a Solution



what i did:

L = 250kg * m^2
Wf = ?
Wi = 2 rad /sec
r = 1.5 m

i don't know what to do from here
 
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  • #2
You'll need to apply conservation of angular momentum given by Iω.

You should also know that for a point mass, like the duck, its inertia at some distance r is mr2. So you need to get I for the table+duck system.

Then just apply the conservation law.
 

Related to Calculating Final Angular Speed of Rotating Table

1. How do you calculate final angular speed of a rotating table?

To calculate the final angular speed of a rotating table, you need to know the initial angular speed, the final angular position, and the time taken to reach the final position. The formula for calculating final angular speed is: final angular speed = (final angular position - initial angular position) / time taken. This will give you the final angular speed in radians per second.

2. What is the unit of measurement for final angular speed?

The unit of measurement for final angular speed is radians per second (rad/s). This is a unit of angular velocity, which measures the rate at which an object rotates around a fixed axis.

3. How does the mass and shape of the rotating table affect the final angular speed?

The mass and shape of the rotating table do not directly affect the final angular speed. However, they can affect the moment of inertia of the table, which is a measure of its resistance to changes in its rotational motion. The higher the moment of inertia, the slower the table will rotate for a given torque, and vice versa.

4. Can the final angular speed of a rotating table change over time?

Yes, the final angular speed of a rotating table can change over time. This can happen if an external force, such as friction or air resistance, acts on the table, causing it to slow down or speed up. It can also change if the initial or final angular positions are adjusted, or if the time taken to reach the final position is altered.

5. How is final angular speed different from initial angular speed?

Final angular speed and initial angular speed are different because they refer to different points in time during the rotation of the table. Initial angular speed is the speed at which the table is rotating when the measurement begins, while final angular speed is the speed at the end of the rotation, after the table has traveled a certain distance or rotated a certain angle. In other words, initial angular speed is the starting point, while final angular speed is the end point of the rotation.

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