Math Problem Statement
A woman passes through a revolving door with a tangential speed of 1.9 m/s. If she is 0.76 m from the center of the door, what is the door’s angular speed? Answer in units of rad/s.
Solution
To find the angular speed () of the revolving door, we can use the relationship between tangential speed () and angular speed:
where:
- (tangential speed),
- (distance from the center of the door to the woman).
Rearranging for :
Substitute the values:
Answer:
The angular speed of the door is approximately .
Would you like further details or have any questions?
Here are five related questions for further exploration:
- What would be the angular speed if the tangential speed doubled?
- How would the angular speed change if the woman was closer to the center?
- What is the tangential acceleration if she increases her speed uniformly?
- How much time would it take for one full revolution?
- How would the angular velocity be affected if the door had resistance?
Tip: Remember that angular speed can be derived by dividing tangential speed by the radius when objects move in a circular path.
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Math Problem Analysis
Mathematical Concepts
Circular Motion
Angular Speed
Tangential Speed
Formulas
v = r * ω
ω = v / r
Theorems
Relationship between Tangential and Angular Speed
Suitable Grade Level
Grades 10-12
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