TBR Physics Chapter 2 Passage IV

[golgiapparatus88]

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I always read that you don't need to know angular velocity and that kind of stuff for the MCAT. This "space lab" passage threw me for a loop. I'm so confused as to when to use centripetal acceleration = mv^2/r or (omega^2)(r) = angular acceleration.

With one, increasing the radius increases acceleration while the other decreases acceleration! Can someone tell me if this is even worth stressing over?

Edit: I understand that mv^2/r is the same thing as w^2(r) but i'm still confused on when to use each one.

 

[wolverinepwns]

I always read that you don't need to know angular velocity and that kind of stuff for the MCAT. This "space lab" passage threw me for a loop. I'm so confused as to when to use centripetal acceleration = mv^2/r or (omega^2)(r) = angular acceleration.

With one, increasing the radius increases acceleration while the other decreases acceleration! Can someone tell me if this is even worth stressing over?

Edit: I understand that mv^2/r is the same thing as w^2(r) but i'm still confused on when to use each one.

I wouldn't stress too much over that, At most it will be one question on the test! RATHER try to understand what they are talking about. you use omega in case of harmonic motion mostly and the mv^2 in case of centripetal (most mechnical problems)

 

[enoknight]

m*v^2/r = m*w^2*r

It is just a way to interconvert between angular components to linear components. Knowing that both exists in a rotational system is the most important thing. You should know that you can have a constant angular velocity (w) but experience more centripetal force if you increase your radius (e.g. moving further away from the central axis).

I would focus on the practical applications rather than the specifics of the equations.

 

[fizzgig]

mv^2/r is centripetal accel, pointing to the center of rotation. it is the acceleration that has to be applied to an orbiting mass at every step to change its direction and keep it in orbit. so as r increases, if the speed of the object doesn't change, the radius of curvature of the orbit is larger, so you have to change the object's direction less with each timestep. note that when you make this change, since speed is the same, your time to complete an orbit will increase.

omega is angular velocity. if you have an object in orbit at a given angular velocity, it will take a certain time t to complete an orbit. this is how many *radians* you're covering in a second, regardless of object distance from point of rotation. if you increase r in this case, if the angular velocity does not change, the object suddenly has to cover more distance in the same time period (because at r=1 or r=100, omega=2pi rad/s means you have to make a full orbit in 1 second). in this case, the time to complete an orbit does not change, because the number of radians in an orbit does not change. the number of meters/s in an orbit has changed, however, since the circumference of the circle changed. in this case the speed of the object must have increased.

hope that makes sense.