12/14/2023 0 Comments Rotational motionThe are only true if the angularĪcceleration is constant, but if it is constant, And then I'll finish cleaning up these v initial and v finals. We replace all of our accelerations with angular accelerations. So I'll replace all these x's with thetas. Was the regular position, you'd replace it with And so you can keep goin' through, wherever you had an x, that When are these rotational motion kinematic formulas gonna be true? It's gonna be when the alpha, the angular acceleration is constant. Only one time and that's t and that works in either equation. So there's no such thing asĪngular time or linear time. The initial velocity, I'd have the initial angular velocity. Of V, the velocity, the final velocity, I would have omega, the final angular velocity. Of these linear variables with their rotational motion Motion kinematic formulas simply by replacing all Linear motion variables, I can make rotational Is the same as the relationship between the Relationship between all these rotational motion variables Using areas under curves, but since we know the Trouble that we went through with these to derive them Kinematic formulas, you could go though the But if the acceleration is constant, these four kinematic formulasĪre a convenient way to relate all these kinematic These equations only work if the acceleration is constant. These are the four kinematicįormulas that relate the linear motion variables. Replaced with its rotational motion variable. Same equations, just with the linear motion variable Motion variables are defined, we're gonna get the exact These are all defined the same way the linear Kinematic formulas, but we already know since Relate it to omega and alpha and we'd get the rotational We could do the same thing for the rotational motion variables. Was by looking for areas under a velocity graph. Kinematic formulas that related these linear motion variables, And so if you rememberįrom 1D motion, the way we derived a lot of the 1D So that means that theĪrea under the curve on a omega versus time graph,Īn angular velocity versus time graph is gonna represent Similarly the area underneath the curve on a velocity versus time graph represented the displacement. The angular acceleration, because the relationshipīetween omega and alpha is the same as the Velocity versus time graph, the slope is going to represent Is equal to the acceleration, that means on an angular Motion that the slope of this velocity versus time graph Velocity versus time graph and it looked like this. In that equation with its rotational motion variable counterpart. Variables as long as you replace the linear motion variable Variables will also hold true for the rotational motions Principles we found and derived for the linear motion The linear motion variable is replaced with its angular counterpart, all the equations results in Just like regular acceleration was the change in regularĭefinitions are exactly the same except for the fact that Was the change in the angular velocity per time, Time just like velocity was the regular displacement over time. Similarly this angular velocity was the angular displacement per This is the angular position as opposed to the position, So for instance, this angular displacement was defined the exact same way we defined regular displacement, it's just The same way we defined all these linear motion variables. Rotational motion variables and we defined them exactly Previous couple videos, we defined all these new
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