A man runs along a circular path of radius 50 m with a linear velocity of 2.5 m/s. What is his angular speed?
Understand the Problem
The question is asking to find the angular speed of a man running along a circular path using his linear velocity and the radius of the path. Angular speed can be calculated using the formula: angular speed = linear velocity / radius.
Answer
The angular speed is $\omega = 0.05 \, \text{rad/s}$.
Answer for screen readers
The angular speed of the man running along the circular path is $\omega = 0.05 , \text{rad/s}$.
Steps to Solve
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Identify the given values
- Linear velocity ($v$) = 2.5 m/s
- Radius of the circular path ($r$) = 50 m
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Use the formula for angular speed The formula for angular speed ($\omega$) is given by: $$ \omega = \frac{v}{r} $$
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Substitute the values into the formula Substituting the known values into the formula: $$ \omega = \frac{2.5 , \text{m/s}}{50 , \text{m}} $$
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Calculate the angular speed Compute the value: $$ \omega = 0.05 , \text{rad/s} $$
The angular speed of the man running along the circular path is $\omega = 0.05 , \text{rad/s}$.
More Information
The angular speed indicates how quickly the man is moving around the circle. It is measured in radians per second, a standard unit in circular motion.
Tips
- Mistaking linear velocity for angular velocity: It's important to remember that angular speed requires conversion via the radius.
- Forgetting units: Always ensure that the units for linear velocity and radius are compatible (e.g., both in meters).
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