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Consider a rotating object. On that object, select a single point that rotates. How does the angular velocity vector of that point compare to the linear velocity vector at that point

User Accraze
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2 Answers

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Final answer:

The angular velocity of a point on a rotating object is related to its linear velocity by the equation ut = rw, where u is the linear velocity, t is the time taken, r is the radius, and w is the angular velocity. The point near the edge of the object will have a greater angular velocity, while the point near the center will have a higher linear velocity.

Step-by-step explanation:

Let's compare the linear and rotational variables individually. The linear variable of position has physical units of meters, whereas the angular position variable has dimensionless units of radians. The linear velocity has units of m/s, and its counterpart, the angular velocity, has units of rad/s. In circular motion, the angular velocity is related to the linear velocity by the equation ut = rw, where u is the linear velocity, t is the time taken, r is the radius, and w is the angular velocity.

Based on this equation, it can be concluded that the point near the edge of the rotating object would have a greater angular velocity, while the point near the center would have a higher linear velocity.

User Praveen Vijayan
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8 votes

Answer:

v = w r

Step-by-step explanation:

The linear and angular variables are related, specifically the linear velocity is equal to the angular velocity multiplied vectorially by the radius

v = w x r

in general if the radius and the angular velocity are perpendicular

sin 90 = 1

v = w r

User Sami Liedes
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