# Determine the tangential and radial acceleration of the car

## Homework Statement

A car at the Indianapolis 500 accelerates uniformly from the pit area, going from rest to 250 km/h in a semicircular arc with a radius of 230 m.

Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration.

r=230m
v1=0 m/s
v2= 250km/h --> 69.44m/s

## Homework Equations

a=r $$\alpha$$

Vtangent=$$\sqrt{\frac{GM}{r}}$$

## The Attempt at a Solution

w1= $$\frac{v1}{r}$$=0

w2=$$\frac{v2}{r}$$=$$\frac{69.44m/s}{230m}$$=0.302rad/s

(.302)2= 02 + 2 ($$\pi$$/2) $$\alpha$$

$$\alpha$$ = .02903 radan/s2

I got this for my TANGENT: (230m)(.02903radan/s2) = 6.68m/s2

and this is my RADIAL:$$\alpha$$ = 0.0290m/s2

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alphysicist
Homework Helper
Hi kblue!1,

## Homework Statement

A car at the Indianapolis 500 accelerates uniformly from the pit area, going from rest to 250 km/h in a semicircular arc with a radius of 230 m.

Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration.

r=230m
v1=0 m/s
v2= 250km/h --> 69.44m/s

## Homework Equations

a=r $$\alpha$$

Vtangent=$$\sqrt{\frac{GM}{r}}$$

## The Attempt at a Solution

w1= $$\frac{v1}{r}$$=0

w2=$$\frac{v2}{r}$$=$$\frac{69.44m/s}{230m}$$=0.302rad/s

(.302)2= 02 + 2 ($$\pi$$/2) $$\alpha$$
The speed of .302rad/s corresponds to when the car has moved through the semicircular path, so I don't think the angle is pi/2 here.

$$\alpha$$ = .02903 radan/s2

I got this for my TANGENT: (230m)(.02903radan/s2) = 6.68m/s2

and this is my RADIAL:$$\alpha$$ = 0.0290m/s2
The alpha value is the angular acceleration; the radial acceleration that the question asks for is related to the radius and the angular velocity. What formula does it have?

the formula for radial acceleration is V^2/r

The speed of .302rad/s corresponds to when the car has moved through the semicircular path, so I don't think the angle is pi/2 here.
Is it just pi?

alphysicist
Homework Helper

the formula for radial acceleration is V^2/r

Is it just pi?
Yes, it would be pi (since the speed of 0.302 rad/s is after the car has moved through an angle of pi).

The radial acceleration is v^2/r like you have; this is also equivalent to

$$a_r=r\ \omega^2$$
so you can find either v or $\omega$ at the halfway mark, whichever you prefer.