EDIT: I meant radial in the title.(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

A ball is going around in a circle of radius 4 m.

It goes with a constant angular velocity of (13 rad/s)[tex]\hat{k}[/tex] for 0.5 s. After that, it takes 4 s to come to a complete stop.

Find the radial component of the ball's acceleration at 2 s.

2. Relevant equations

3. The attempt at a solution

My book says that to use the formula a_{r}= w^{2}r. However, w is changing, so I don't see how I can use that!

The only thing I can think of is to find the angular acceleration:

[tex]\alpha[/tex] = w_{0}+ [tex]\alpha[/tex]_{0}(t)

0 = (13 rad/s) + [tex]\alpha[/tex]_{0}(4 s). Solving for [tex]\alpha[/tex] gives -3.25 rad/s^{2}[tex]\hat{k}[/tex]

Then I use another formula to find the angular velocity at 2 s:

w_{final}= w_{initial}+ [tex]\alpha[/tex](t)

w_{f}= (13 rad/s) + (-3.25 rad/s^{2})(2 s)

w_{f}= 6.5 rad/s [tex]\hat{k}[/tex]

Then use that first formula:

a_{r}= (6.5 rad/s)^{2}(4 m)

a_{r}= (169 rad/sm)[tex]\hat{k}[/tex]

Are those units correct? Really the formula for a_{r}= dVt / dt, but is what I did ok?

Also, as an aside, the TANGENTIAL part of the angular acceleration would stay the same all the time, right? If I calculated it at 1 s, 2s, ... 4.3 s, it would not change?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Finding the tangential component of acceleration

**Physics Forums | Science Articles, Homework Help, Discussion**