Calculating Angular Velocity and Kinetic Energy in a Rotating System

In summary, the student is sitting on a rotating stool with two 2 kg masses positioned 0.78 m from the axis of rotation, resulting in an angular velocity of 1.7 rad/sec. When the masses are pulled in to 0.25 m from the rotation axis, the student's angular velocity increases to omega2. The combined momentum of inertia for the student and stool is 1.8 kg*m^2. Using the formula I1*Omega1=I2*Omega2, the new angular velocity omega2 can be calculated. The student also performs mechanical work, increasing the kinetic energy of the system. The increase in kinetic energy can be calculated using the formula KE=1/2*m*v^2
  • #1
BARBARlAN
9
0

Homework Statement


A student sits on a rotating stool holding two 2 kg masses. When his arms are extended horizontally, the masses are 0.78 m from the axis of rotation, and he rotates with an angular velocity of 1.7 rad/sec. The student then pulls the weights horizontally to a shorter distance 0.25 m from the rotation axis and his angular velocity increases to omega2. For simplicity, assume the student himself plus the stool he sits on have constant combined momentum of inertia I(subscript s) = 1.8kg*m^2. Find the new angular velocity omega2 of the student after he has pulled in the weights. Answer in units of rad/s.

When the student pulls the weights in, he performs mechanical work - which increases the kinetic energy of the rotating system. Calculate the increase in the kinetic energy. Answer in units of J.


Homework Equations


I1*Omega1=I2*Omega2
KE=1/2*m*v^2+1/2*I*omega^2


The Attempt at a Solution


I'm not sure of I*omega is the right formula, because it seems the moment of inertia stays constant throughout. So I'm stuck.
 
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  • #2
BARBARlAN said:
I'm not sure of I*omega is the right formula, because it seems the moment of inertia stays constant throughout. So I'm stuck.

What's the moment of inertia of a 2kg mass at a radius of 0.78 m from the axis of rotation?
How about when it is at 0.25 m?
 
  • #3
1.2168 kg*m^2 at .78m, .125 kg*m^2 at .25m. How does this help though when I don't know the mass of the stool or the person?
 
  • #4
ok i got part 1 right. any tips on how to do part 2?
 
  • #5
BARBARlAN said:
1.2168 kg*m^2 at .78m, .125 kg*m^2 at .25m. How does this help though when I don't know the mass of the stool or the person?

You're given their moment of inertia. For angular motion this plays the same roll as mass.

Try to determine the rotational kinetic energy for the first situation: weights held at 0.78m and rotation rate 1.7 rad/sec. Show your work!
 
  • #6
ok I got it right! Thank you all very much :)
 

1. What is the Angular Momentum problem?

The Angular Momentum problem is a concept in physics that refers to the conservation of angular momentum in a closed system. Angular momentum is a measure of an object's rotational motion, and according to the law of conservation of angular momentum, the total angular momentum of a system remains constant unless an external torque is applied.

2. Why is the Angular Momentum problem important?

The Angular Momentum problem is important because it helps us understand the behavior of rotating objects and systems. It also plays a crucial role in various fields of physics such as mechanics, astrophysics, and quantum mechanics.

3. How is the Angular Momentum problem solved?

The Angular Momentum problem is solved by applying the law of conservation of angular momentum, which states that the total angular momentum of a system remains constant. This means that if there is no external torque acting on a system, the initial angular momentum will be equal to the final angular momentum.

4. What are some real-world examples of the Angular Momentum problem?

Some real-world examples of the Angular Momentum problem include the rotation of the Earth around its axis, the orbit of planets around the sun, and the spin of a spinning top.

5. How does the Angular Momentum problem relate to the conservation of energy?

The Angular Momentum problem is closely related to the conservation of energy. The law of conservation of angular momentum is a consequence of the law of conservation of energy, which states that energy cannot be created or destroyed, only transferred or transformed. In a closed system, any changes in angular momentum must be accompanied by a corresponding change in energy.

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