Two problems involving angular velocity:

In summary, there were two problems discussed in the conversation. The first problem was solved successfully, while the second problem involved calculating the speed of the Sun with respect to the center of the Milky Way galaxy. The correct answer was eventually found by converting the units from km/year to km.
  • #1
Bob Loblaw
69
0
Two problems involving angular velocity:

Edit: Problem one solved! Hooray!

2.The Milky Way galaxy rotates about its center with a period of about 192 million years. The Sun is 2x10^20 m from the center of the galaxy. How fast is the Sun moving with respect to the center of the galaxy?

For this problem I took 2pi/T which gave me 2pi/192000000 and multiplied the result by 2x10^20m. I then expressed the answer in kilometers which gave me 6544984695km. This was not correct. Any suggestions?

Thanks for your generous help!
 
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  • #2
The number you have is in units of km/year... are these the units you need?
 
  • #3
Yes - it was indeed a problem of units. I took 2pi/(195 million years)(second in a year) * 2.0x10^20 and came up with the correct answer once I converted centimeters into kilometers.

Thanks!
 

FAQ: Two problems involving angular velocity:

What is angular velocity?

Angular velocity is a measure of the rate of change of angular displacement over time. It describes the speed at which an object is rotating around a central point.

How is angular velocity calculated?

Angular velocity is calculated by dividing the change in angular displacement by the change in time. It is typically measured in radians per second (rad/s) or degrees per second (deg/s).

What is the difference between angular velocity and linear velocity?

Angular velocity refers to the rotational motion of an object, while linear velocity refers to the straight-line motion of an object. Angular velocity is measured in radians or degrees per second, whereas linear velocity is measured in meters or feet per second.

How does angular velocity affect centripetal force?

Angular velocity and centripetal force are directly related. As the angular velocity of an object increases, so does the centripetal force required to keep it moving in a circular path. This is because centripetal force is what causes an object to change its direction and move in a curved path.

What are some real-world examples of problems involving angular velocity?

Some real-world examples of problems involving angular velocity include the rotation of a car's tires, the spinning of a record on a turntable, and the motion of a Ferris wheel. In each of these cases, the objects are rotating around a central axis and their angular velocity can be calculated to determine their speed and direction of rotation.

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