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cscott
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Why do we use the angle as the base quantity in rotational dynamics instead of, perhaps, arc length? Is it because angular displacement is easier to measure? Would it make any sense to use arc length?
ZapperZ said:Arc length depends on the radius that you choose, so you always have to indicate the radius you are using that corresponds to that arc length. Angular displacement doesn't.
Zz.
Angular displacement is a measurement of the change in the angle of an object's position in rotational motion. It is typically measured in radians or degrees.
Angular displacement measures the change in angle, while linear displacement measures the change in distance. Angular displacement is specific to rotational motion, while linear displacement can occur in both rotational and linear motion.
Angular displacement, rotational velocity, and rotational acceleration are all related through the equations: ω = Δθ/Δt and α = Δω/Δt. This means that angular displacement is directly proportional to rotational velocity and the change in rotational velocity is directly proportional to rotational acceleration.
Angular displacement has a direct relationship with an object's moment of inertia. As the angular displacement increases, the moment of inertia also increases. This means that it becomes more difficult to change the rotational motion of an object with a larger moment of inertia.
Angular displacement is used in various real-world applications, such as in the design and analysis of rotating machinery, vehicles, and structures. It is also used in fields such as robotics, aerospace engineering, and physics to study the motion of rotating objects.