Calculating Angular Velocity: Puck in Circular Motion

In summary, a puck with a mass of 0.28 kg is moving in a circle with a radius of 0.75 m, at an angular velocity of 18 rad/s. When the radius is reduced to 0.55 m, the new angular velocity of the puck is 33.47 rad/s. The moment of inertia of the puck does not need to be considered as the problem treats the puck as a point mass and the conservation of angular momentum equation can be used to solve for the new angular velocity.
  • #1
zoner7
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Homework Statement



A puck with mass 0.28 kg moves in a circle at the end of a string on a frictionless table, with radius 0.75 m. The string goes through a hole in the table, and you hold the other end of the string. The puck is rotating at an angular velocity of 18 rad/s when you pull the string to reduce the radius of the puck's travel to 0.55 m. Consider the puck to be a point mass. What is the new angular velocity of the puck?

The Attempt at a Solution



So we clearly have a centripetal force here caused by the pull of the string.
ooo... definitely just realized that I was given the mass. I was going to ask how in the world is the problem solvable without it. let me work some more and see what I come up with.

So, I believe that the centripetal acceleration is linear not angular. I need to somehow relate this linear acceleration to the change angular velocity and radius...

By the way, is it necessary to consider moment of inertia, or does it not matter because the object is already in motion? But since the object is accelerating...

Are there any good websites that explain moment of inertia nicely? I still do not completely understand it.
 
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  • #2
So I browsed through my physics book and stumbled upon the concept of conservation of angular momentum.

Li = Lf
Iiωi = Ifωf

Although I have no idea what the moment of inertia of a puck is, i concluded that it is irrelevant because everything except the radii and the angular velocities cancel once you compare the two equations.

So I said that
Ri^2 * wi = Rf^2 * wf

Plugging in my values I got
0.75^2 * 18 = 0.55^2 * wf
Solving for wf I got 33.47 rad/s.

seems a little big to me. And, more importantly, I never even used the mass, which was given to me. Can anyone spot my error?
 
  • #3
Just because the mass is given, it doesn't mean you have to use it:smile:

The moment of inertia of the puck does not matter because the problem asks you to treat it as a point mass.

Your solution looks fine to me.
 
  • #4
thank you :)
Trying to trick me with that given mass...
those problem designers are a little evil
 
  • #5
I believe you must use inertia. In the simplest form - that of a point mass, I=ms*r^2.
Your problem is that when r changes, so does I (as a squared function), so L also changes. To conserve L, w changes according to w=L/I
 
  • #6
(Sorry, I meant the moment of inertia of the puck about its own axis in my prev post)
 

FAQ: Calculating Angular Velocity: Puck in Circular Motion

What is angular velocity?

Angular velocity is the rate at which an object rotates or spins around a fixed point. It is typically measured in radians per second (rad/s) or degrees per second (deg/s).

How do you calculate angular velocity?

Angular velocity can be calculated by dividing the change in the angle (in radians or degrees) by the change in time. The formula is: ω = Δθ / Δt

What is the difference between angular velocity and linear velocity?

Angular velocity is a measure of rotational speed, while linear velocity is a measure of how fast an object is moving in a straight line. Angular velocity is typically measured in units of rotation per time, while linear velocity is measured in units of distance per time.

How does angular velocity relate to circular motion?

Angular velocity is a crucial component in circular motion as it determines the speed at which an object is rotating around a fixed point. It is also responsible for the centripetal acceleration necessary to keep the object in circular motion.

Can angular velocity be negative?

Yes, angular velocity can be negative if the object is rotating in a clockwise direction. This is because the direction of the rotation is taken into account when calculating angular velocity, with counterclockwise rotations being positive and clockwise rotations being negative.

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