TBR physics concept help, uniform circular motion pg 81

[silverice]

I didn't understand the paragraph right above equation 2.25 delta V= V* delta theta

The last sentence said If the angle in radians is very small, then the arc length (lets use deltaV) divided by the radius (let's use V) is the angle delta theta, equation (2.25).

I don't understand why do we use V as radius. If we can use V in place of radius then the equation for centripetal acceleration ac=V^2/r made no sense, because we then can use r to substituted V, we would get r^2/r.

I'm very confused, please help.

Besides, how long does it take you guys to go over a chapter of TBR, only the content, no practice. I always ended up use almost the whole day to study the content, from 8am to 5 pm. then I would get so drained and tired to do practice questions.

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[MedPR]

I didn't understand the paragraph right above equation 2.25 delta V= V* delta theta

The last sentence said If the angle in radians is very small, then the arc length (lets use deltaV) divided by the radius (let's use V) is the angle delta theta, equation (2.25).

I don't understand why do we use V as radius. If we can use V in place of radius then the equation for centripetal acceleration ac=V^2/r made no sense, because we then can use r to substituted V, we would get r^2/r.

I'm very confused, please help.

Besides, how long does it take you guys to go over a chapter of TBR, only the content, no practice. I always ended up use almost the whole day to study the content, from 8am to 5 pm. then I would get so drained and tired to do practice questions.

I don't know if this is right, but it's how I rationalized it when I read it.

Theta = S/r

As theta approaches 1, the difference between S and r becomes smaller and smaller.

S = deltav as shown in figure 2.1. As the value for S approaches the value for r (as theta approaches 1), r becomes v.

It's really just a derivation of the equation a=v^2/r. You don't need to understand it to be successful on these problems.

I spend more time doing problems than I do trying to understand the concept based on reading about it alone. I learn more (and more quickly) by doing problems, getting them wrong, then figuring out why I got them wrong.

 

[silverice]

I don't know if this is right, but it's how I rationalized it when I read it.

Theta = S/r

As theta approaches 1, the difference between S and r becomes smaller and smaller.

S = deltav as shown in figure 2.1. As the value for S approaches the value for r (as theta approaches 1), r becomes v.

It's really just a derivation of the equation a=v^2/r. You don't need to understand it to be successful on these problems.

I spend more time doing problems than I do trying to understand the concept based on reading about it alone. I learn more (and more quickly) by doing problems, getting them wrong, then figuring out why I got them wrong.

Thank you very much for your help. yeah, I was thinking I need to modify my study method as well. I definitely need to spend more time to do problems.

Thanks