Angular velocity concept question

AI Thread Summary
Angular velocity is defined as the angle per unit time, and it is the same for both clocks regardless of their size because they complete a full rotation (360°) in the same time period. The formula for angular velocity, ω = v/r, indicates that while the radius (r) of Big Ben is larger, the linear velocity (v) at the end of the clock hand is also proportionally greater due to its length. Therefore, despite the difference in radius, the angular velocities remain equal. This concept highlights the relationship between linear velocity and radius in the context of rotational motion. Understanding this principle clarifies why both clocks exhibit the same angular velocity.
idllotsaroms
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The Attempt at a Solution



How are their angular velocities the same? I thought Angular velocity = v/r where v = velocity and r = radius.
In this case isn't the radius of big ben much larger and therefore have a much smaller angular velocity?
 
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hi idllotsaroms! :smile:
idllotsaroms said:
How are their angular velocities the same? I thought Angular velocity = v/r where v = velocity and r = radius.
In this case isn't the radius of big ben much larger and therefore have a much smaller angular velocity?

angular velocity means angle per time

doesn't each clock goes 360° in the same time? :wink:

(and the speed, v, at the end of the hand is proportional to the length of the hand)
 
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