How to Solve for Distance and Time in Rotational Motion Problems

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The discussion focuses on solving two rotational motion problems involving a coin and a race car. For the coin, the user struggles to calculate the distance it rolls before stopping, initially using incorrect formulas and values. The correct approach involves applying uniform acceleration kinematics and understanding angular motion equations. In the second problem, the user is confused about the relationship between centripetal and tangential accelerations and how to find the speed and distance traveled by the race car. The thread highlights the need for clarity in applying physics concepts and formulas to solve these problems effectively.
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Okay, I first want to tell you that today is my birthday so if you want to doubley help me out, that would be great...
so i put my homework off because it was my homework weekend and now I'm screwed because i can't figure out these last two problems.

1.) A coin with a diameter of 2.40 cm is dropped on edge onto a horizontal surface. The coin starts out with an initial angular speed of 18 rad/s and rolls in a straight line without slipping. If the rotation slows with an angular accelerationb of magnitude 1.9rad/s^2, how far does the coin roll before coming to rest?
Answer: 1.2m
My work: chicken scratch-- I don't think I've done anything right. I know the radius is .012m and W initial is 18 rad/s and I think W final is 0, right? Alpha is 1.9rad/s^2 (or is this considered negative because it is slowing?) I have no idea what theta is, or the time... I guess If I could solve for time, I'd be able to solve for theta, but I can't figure out how to solve for time seeing there is no theta distances. PLEASE HELP! I WANT TO CELEBRATE MY BIRTHDAY! : )

2.) A race car starts from rest on a circular track of radius 400 m. The car's speed increases at the constant rate of .500m/s^2. At the point where the magnitudes of the centripetal and tangential accelerations are equal, determine (a) the speed of the car, (b) the distance traveled, and (c) the elasped time.

I know a) Ac= v so .5=V^2/400 which gives v = 14.1 m/s

B) ? I don't understand centripetal and tangential accelerations are equal? I'm stuck here, so I'm obviously stuck for c.

Thanks to anyone who can help me out here...
 
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Happy Birthday! :biggrin:

1) Use uniform acceleration kinematics formula

\omega^2 = \omega^2_{o} + 2 \alpha\theta

Use too

s = r\theta

2)

Vector quantities

A^2 = A^2_{r} + A^2_{t}

Also

A_{r} = \frac{v^2}{r}

A_{t} = \frac{\Delta |v|}{\Delta t}
 
Last edited:
okay, i did what you said for #1... but my answer is off .
18^2 =2(1.9)theta... I got 85.3 and then multiplied that by .012 for the radius and got 1.0236. The answer is 1.2m... Where did I go wrong? And for #2, I'm still totally confused and not getting the right answers
 
yes, i did ask but i didn't look! Thanks for the help, I'm sure it will help. Any help with the next problem?? My sister is even trying to help me with it and we are not getting anywhere! Just further into our block whole of physics torture!
 
Actually, I got the wrong answer again! 1.02 and it's supposed to be 1.2! Maybe that's a mistake... Looking forward to more help! : )
 

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