Angular velocity of a small object

In summary, the object will get faster and faster, just like an ice-skater turns faster when she pulls her arms in. At the bigger radius, the angular momentum is 521.37.
  • #1
maevis18
3
0
A small 0.870-kg object moves on a frictionless horizontal table in a circular path of radius 7.80 m. The angular speed is 9.85 rad/s. The object is attached to a string of negligible mass that passes through a small hole in the table at the center of the circle. Someone under the table begins to pull the string downward to make the circle smaller. If the string will tolerate a tension of no more than 1140 N, what is the radius of the smallest possible circle on which the object can move?



Can anyone help? i don't even know where to start. Help is greatly appreciated. :)
 
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  • #2
Welcome to PF!

maevis18 said:
A small 0.870-kg object moves on a frictionless horizontal table in a circular path of radius 7.80 m. The angular speed is 9.85 rad/s. The object is attached to a string of negligible mass that passes through a small hole in the table at the center of the circle. Someone under the table begins to pull the string downward to make the circle smaller. If the string will tolerate a tension of no more than 1140 N, what is the radius of the smallest possible circle on which the object can move?

Hi maevis18! Welcome to PF! :smile:

Hint: The object will get faster and faster, just like an ice-skater turns faster when she pulls her arms in.

How fast can it go before the string breaks? :smile:
 
  • #3
thanks for that.

hmmm- I am assuming the angular momentum in both cases is the same.
I worked out the moment of inertia of the object at the bigger radius.
I = mr /2
(0.870)(7.8/2)
52.9308

angular momentum = (52.9308)(9.85)
= 521.37

any idea on where to go from here??
 
  • #4
maevis18 said:
thanks for that.

hmmm- I am assuming the angular momentum in both cases is the same.
I worked out the moment of inertia of the object at the bigger radius.
I = mr /2
(0.870)(7.8/2)
52.9308

angular momentum = (52.9308)(9.85)
= 521.37

any idea on where to go from here??

Yes … but you go first! :biggrin:
 

FAQ: Angular velocity of a small object

What is angular velocity?

Angular velocity refers to the rate at which a small object rotates around a fixed point or axis. It is usually measured in radians per second or degrees per second.

How is angular velocity different from linear velocity?

While linear velocity measures the speed of an object in a straight line, angular velocity measures the rotational speed of an object around a fixed point.

What factors affect the angular velocity of a small object?

The angular velocity of a small object can be affected by the object's moment of inertia, the radius of its circular motion, and any external forces acting on it.

How is angular velocity calculated?

Angular velocity is calculated by dividing the change in the object's angular displacement by the change in time. It can also be calculated by dividing the object's linear velocity by the radius of its circular motion.

Why is angular velocity important in physics?

Angular velocity is an important concept in physics because it is used to describe the rotational motion of objects, which is present in many real-world scenarios such as the motion of planets, gears, and spinning tops.

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