Force in relation to angular momentum

In summary: Work done equals KE multiplied by the distance moved.In summary, the student is sitting on a spinning stool with a 2kg dumbbell in each hand. The angular velocity is 3rad/sec. The arms are stretched out to a radius of 80cm and he pulls them in to 20cm. He then calculates the force he needs to pull the weight in at a constant speed and finds it is equal to 7.68*(184.32-11.52)*20cm= 5,069N.
  • #1
valvan1
3
0

Homework Statement



so a student is sitting on a spinning stool and has a 2kg dumbbell in each hand angular velocity is 3rad/sec arms stretched out is a radius of 80cm and he pulls in his arms to 20cm. for this problem your ignoring the students weight.

from other problems i have figured out
so angular velocity to start with is 3 rad/sec
angular velocity final is 48 rad/sec

kinetic energy initial is 11.52( don't know what this dimensions is so I am guessing J)
kinetic energy final is 184.32
angular momentum = 7.68

and i need to find the force required to pull one of the dumbbells in at a constant speed is equal to F=((initial angular momentum of 1 block)^2)/(4*Mass of one weight*Radius^3))

Homework Equations


I=[tex]\sum[/tex]mr^2
k=1/2I[tex]\omega[/tex]^2
[tex]T[/tex]=I[tex]\alpha[/tex]
L=I[tex]\omega[/tex]

The Attempt at a Solution


do i say Torque=F*d and Torque=I*alpha and then go Force = Ia/d? or is there another way to solve this that I am not seeing ?
or do i use the change in kinetic energy equation 1/2*I*[tex]\omega[/tex]^2Final-1/2*I*[tex]\omega[/tex]^2initial = F*d
 
Last edited:
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  • #2
I would think the change in kinetic energy would be equal to the work done in moving the dumbell from 80cm to 20 cm.
 
  • #3
Yes, KE would increase when moved from 80cm to 20cm. It would increase 16 times!

The KE is gained at the expense of work done overcoming the radial inertial force (m * w^2 * r) along a distance 60 cms. w = angular velocity. As the dumbell is moving from 80 to 20, the angular velocity increases to satisfy the angular momentum conservation. So "w" at any radial distance is given by w(r) = w(R) * (R/r)^2

where w(R) is the angular velocity at radius R. If we put this inertial force and work done in moving infinitesimal distance "dr" then we get a definite integral that gives the work done to increase the KE from bringing the dumbell from 80cms to 20cms
 
Last edited:

What is force in relation to angular momentum?

Force in relation to angular momentum is the external force applied to an object that causes it to rotate around an axis. It is a vector quantity that has both magnitude and direction.

How does force affect angular momentum?

Force affects angular momentum by changing the speed or direction of rotation of an object. When a force is applied perpendicular to the axis of rotation, it causes the object to rotate faster or slower depending on the direction of the force.

What is the relationship between force and angular momentum?

The relationship between force and angular momentum is that force is directly proportional to the rate of change of angular momentum. This means that the greater the force applied, the greater the change in the object's rotational speed or direction.

What is the difference between linear and angular momentum?

Linear momentum is the product of an object's mass and velocity, while angular momentum is the product of an object's moment of inertia and angular velocity. Linear momentum involves the movement of an object in a straight line, while angular momentum involves the rotation of an object around an axis.

How is angular momentum conserved?

Angular momentum is conserved when there is no external torque acting on an object. This means that the initial angular momentum of an object will remain constant unless an external force is applied to change it. This is known as the law of conservation of angular momentum.

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