Centripetal and Tangencial Accelaration

[martcapt]

Homework Statement

English is not my first language from the beginning I apologize for any mistakes in scientific terms, anyhow.
Car with 500kg.
No initial velocity, and from origin or the referential.
Circular track, 50m radius.
The module of the velocity increases in 2m/s

Homework Equations

I can't post the damn symbols for some reason but I believe this is a very simple problem.. Sorry

The Attempt at a Solution

Well there are three parts
Indication of the angular position
Indication of the angular velocity after a lap.
Indication of the time in witch the centripetal acceleration is the same as the tangential acceleration

The first two I'm pretty sure of the results it gave me 0.02t(squared) on the first and angular velocity=0.7rad/s on the second, if someone would be as so kind as checking this I would really apreciate it, but the problem in witch I'm having trouble is the third, this is the only thing I have done so far:

at=ac
2=v(squared)/r
v=10

sorry for bothering, but my teacher has the bad habit of giving exercises with no solution and I would really apreciate one for this one :)

Anyways so as to not create another thread if someone happens to know some condensed but thorough material in two dimensional motion, it would be great :)
thanks.

 

[Andrew Mason]

You have to be a little clearer in stating the problem. I gather that the tangential acceleration is 2 m/sec^2. Is the first question: what is the angular position as a function of time? Is the second question: what is the angular velocity after one complete rotation ie through an angle of [itex]2\pi [/itex] radians? and is the third question: at what time will the centripetal acceleration be equal in magnitude to the tangential acceleration?

AM

 

[martcapt]

Correct on all three.
Sorry,I'm not used to writing this stuff in text, and in english

 

[Andrew Mason]

Correct on all three.

Then your answers to the first two questions are correct.

AM

 

[asteriatic]

No problem, I can help with this problem. First, let's define the terms centripetal and tangential acceleration. Centripetal acceleration is the acceleration towards the center of a circular motion, while tangential acceleration is the acceleration along the tangent of the circle. In this problem, the car is moving in a circular track with a radius of 50m and an initial velocity of 0 m/s. After one lap, the velocity increases by 2 m/s, resulting in a new velocity of 2 m/s.

To find the angular velocity, we can use the formula w=v/r, where w is the angular velocity, v is the linear velocity, and r is the radius. Plugging in the values, we get w=2m/s/50m=0.04 rad/s.

Now, to find the time in which the centripetal acceleration is equal to the tangential acceleration, we can set the two equations equal to each other. Since the car is moving in a circular motion, we know that the tangential acceleration is equal to the change in velocity over the change in time. So, we can set the equation for tangential acceleration (at) equal to the equation for centripetal acceleration (ac).

at = ac
2m/s^2 = v^2/r
2m/s^2 = (2m/s)^2/50m

Solving for t, we get t=5 s. So, after 5 seconds, the car will have the same centripetal and tangential acceleration.

As for condensed material on two-dimensional motion, I would recommend looking at online resources such as Khan Academy or Physics Classroom. They have concise explanations and practice problems that can help with understanding the concepts. Hope this helps!