Angular Momentum, Inertia and Kinetic Energy?

In summary: What are the variables in the linear motion equation? Please wait for the OP to respond to the initial hint before providing additional help. Forum rules require that an attempt at a solution or at least a solid demonstration of effort be shown before help can be given.Clearly, there is a "initial" and "final" situation.Can you try to identify what quantities are important in this problem?What are those quantities (in terms of what is given) for the "initial" and "final" situations?If there are unknowns, what laws of physics would be useful to relate the unknowns to the givens?
  • #1
AndreewL
2
0

Homework Statement



  1. A large wooden turntable in the shape of a flat disk has a radius of 1.50 m and a total mass of 100 kg. The turntable is initially rotating about its vertical axis through its centre with an angular velocity of 2.50 rad/s. From a very small height a 100 kg sand bag is dropped vertically onto the turntable at a point near the outer edge.

    a) Find the angular velocity of the turntable after the sand bag is dropped (assume that the bag can be treated as a point ).

    b) Calculate the kinetic energy of the system before and after the bag is dropped. Why are the kinetic energies not equal?


Homework Equations


I=1/2MR^2

The Attempt at a Solution


I've been stuck on this for a couple days now just playing around with it and haven't seem to get anywhere towards the answer.
 
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  • #2
Hi AndreewL, Welcome to Physics Forums.

You'll have to show some effort, showing what you've attempted during your "playing around with it". What avenues have you explored? What equations have you investigated?

Hint: This is effectively a collision type of problem involving angular motion rather than linear motion. What type of collision it? What is conserved in such collisions?
 
  • #3
Clearly, there is a "initial" and "final" situation.
Can you try to identify what quantities are important in this problem?
What are those quantities (in terms of what is given) for the "initial" and "final" situations?
If there are unknowns, what laws of physics would be useful to relate the unknowns to the givens?
 
  • #4
robphy said:
Clearly, there is a "initial" and "final" situation.
Can you try to identify what quantities are important in this problem?
What are those quantities (in terms of what is given) for the "initial" and "final" situations?
If there are unknowns, what laws of physics would be useful to relate the unknowns to the givens?
Please wait for the OP to respond to the initial hint before providing additional help. Forum rules require that an attempt at a solution or at least a solid demonstration of effort be shown before help can be given.
 
  • #5
robphy said:
Clearly, there is a "initial" and "final" situation.
Can you try to identify what quantities are important in this problem?
What are those quantities (in terms of what is given) for the "initial" and "final" situations?
If there are unknowns, what laws of physics would be useful to relate the unknowns to the givens?

I worked out the initial moment of inertia to be 112.5, I'm just unsure on equations lining angular velocity and Inertia
 
  • #6
AndreewL said:
I worked out the initial moment of inertia to be 112.5, I'm just unsure on equations lining angular velocity and Inertia
What are the corresponding equations for linear motion? The equations for linear and angular motion take the same form, just the corresponding variables are renamed accordingly.
 

1. What is angular momentum and how is it calculated?

Angular momentum is a property of a rotating object that describes its tendency to continue rotating. It is calculated by multiplying the object's moment of inertia by its angular velocity.

2. How does inertia affect an object's motion?

Inertia is the tendency of an object to resist changes in its motion. The greater an object's inertia, the more force is needed to change its speed or direction of motion.

3. What is kinetic energy and how is it related to inertia?

Kinetic energy is the energy an object possesses due to its motion. It is directly related to an object's inertia, as the more mass an object has, the more kinetic energy it has when in motion.

4. How does angular momentum affect the stability of a rotating object?

Angular momentum plays a crucial role in the stability of a rotating object. If the angular momentum is high, the object will be more stable and resistant to changes in its rotation. If the angular momentum is low, the object is more likely to wobble or topple over.

5. Can the conservation of angular momentum be observed in real-life situations?

Yes, the conservation of angular momentum is observed in many real-life situations. For example, an ice skater spinning on one leg will spin faster when pulling their arms in closer to their body, due to the conservation of angular momentum. Another example is a spinning top maintaining its upright position due to its angular momentum.

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