Did I Use the Right Approach for Conservation and Angular Velocity?

In summary, the question involves calculating the angular velocity for a door attached to a rod during a collision. The method used to solve this is conservation of energy, not momentum, which involves finding the moment of inertia. The calculated value for the angular velocity is 18.63 rad/s. The note at the bottom of the question suggests treating the door as a rod rotating about its end and using the equation for inertia, (1/3)ML^2. If the solution is incorrect, assistance is needed.
  • #1
shaqtus
7
0

Homework Statement


I need help with this question: http://img804.imageshack.us/img804/2278/unledsbg.jpg

For a, I got omega = 18.63 rad/s by using methods of conservation of energy. Can someone tell me if I did this right? If not, please help me out! To be honest, I thought I had to use conservation of momentum for this since it involves a collision, but its equations don't involve angular velocity.

Homework Equations



Conservation of energy/momentum

The Attempt at a Solution


a) omega = 18.63 rad/sec
 
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  • #2
Energy is not conserved. But angular momentum is.
 
  • #3
So does that mean I find v by means of conservation of momentum, and then use omega = v / r to find the answer? The reason I'm confused is because at the note at the bottom of the question, it says treat the door as a rod rotating about its end, which is a hint to use Inertia = (1/3)ML^2. Conservation of energy, not momentum, has inertia in its equation.
 
  • #4
shaqtus said:
Conservation of energy, not momentum, has inertia in its equation.
Conservation of angular momentum will involve the moment of inertia.
 
  • #5
is correct. You were correct in using conservation of energy. In this case, the initial energy of the object is equal to its final energy, so we can set the initial kinetic energy equal to the final potential energy.

Initial kinetic energy = 1/2 * m * v^2 = 1/2 * 0.5 kg * (12 m/s)^2 = 36 J
Final potential energy = mgh = 0.5 kg * 9.8 m/s^2 * 2m = 9.8 J

36 J = 9.8 J
v^2 = 2gh
v = sqrt(2gh) = sqrt(2 * 9.8 m/s^2 * 2m) = 6.26 m/s

Since angular velocity is equal to v/r, we can plug in the values to get:
omega = v/r = 6.26 m/s / 0.2 m = 31.3 rad/s

Therefore, your answer of 18.63 rad/s is correct. You were also correct in thinking that conservation of momentum could be used, but it would require additional information such as the mass and velocity of the second object involved in the collision. Using conservation of energy is a simpler and more straightforward approach in this case.
 

FAQ: Did I Use the Right Approach for Conservation and Angular Velocity?

What is conservation of angular velocity?

Conservation of angular velocity is a fundamental law in physics that states that the angular velocity of a system remains constant unless acted upon by an external torque. This means that the rotational speed of an object will remain the same unless a force is applied to change it.

How does conservation of angular velocity apply to objects in motion?

Conservation of angular velocity applies to any object that is rotating or undergoing circular motion. This includes objects such as planets in orbit, wheels on a vehicle, or a spinning top. As long as no external torque is applied, the object will maintain a constant angular velocity.

Why is conservation of angular velocity important in physics?

Conservation of angular velocity is important because it is a fundamental law of motion that helps us understand and predict the behavior of objects in motion. It allows us to mathematically describe the relationship between torque, angular momentum, and rotational speed.

What are some real-world examples of conservation of angular velocity?

One example is the Earth's rotation around its axis, which remains constant unless affected by external forces such as the Moon's gravitational pull. Another example is a spinning top, which will continue to spin at a constant speed unless acted upon by friction or other external forces.

How does conservation of angular velocity relate to conservation of energy?

Conservation of angular velocity is closely related to the law of conservation of energy. Both laws state that energy cannot be created or destroyed, only transferred or transformed. In the case of angular velocity, the total energy of a rotating object remains constant unless an external torque is applied to change it.

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