Question Video: Comparing the Angular Velocities of an Object in Uniform Circular Motion | Nagwa Question Video: Comparing the Angular Velocities of an Object in Uniform Circular Motion | Nagwa

# Question Video: Comparing the Angular Velocities of an Object in Uniform Circular Motion Physics • First Year of Secondary School

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Which of the lines on the graph correctly shows how the angular velocity of an object varies with the radius of the circular path followed by the object? Assume that the linear speed of the object is constant.

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### Video Transcript

Which of the lines on the graph correctly shows how the angular velocity of an object varies with the radius of the circular path followed by the object? Assume that the linear speed of the object is constant. (A) The purple line, (B) the blue line, (C) the gray line, (D) the orange line, (E) none of the answers are correct.

Here, we’re looking at an object that is moving along a circular path. We need to figure out which line on the graph shows how the object’s angular velocity changes as the radius of the circle changes. First, let’s recall the relationship between the radius of the circle along which an object moves, the speed with which it moves, and the angular velocity. 𝜔 equals 𝑣 over 𝑟, where 𝜔 is the angular velocity, 𝑣 is the speed, and 𝑟 is the radius of the circle.

Since we are told the speed 𝑣 is constant, we can simplify this relationship for our object. The angular velocity is inversely proportional to the radius of the circle. In other words, if we were to double the radius of the circle, the angular velocity would halve.

Returning to our graph then, we’re looking for a line that shows a decrease in the angular velocity as the radius increases. On our graph, this would be a line with a negative slope at every point. The blue, gray, and orange lines have a positive slope at every point, while the purple line has a zero slope at every point. None of them even have a negative slope, which means that none of these lines can represent the correct relationship between an object’s angular velocity and the radius of the circle along which it moves if the linear velocity is kept constant.

Therefore, our final answer is option (E). None of the answers are correct.

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