(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

An object of mass m is constrained to move in a circle of radius r. Its tangential acceleration as a function of time is given by [tex]a_{tan} = b + ct^2[/tex], where b and c are constants.

A) If [tex]v = v_0[/tex] at t = 0, determine the tangential component of the force, [tex]F_{\tan }[/tex], acting on the object at any time t > 0.

Express your answer in terms of the variables m, r, [tex]v_0[/tex], b, and c.

B) Determine the radial component of the force [tex]F_{\rm{R}}[/tex].

Express your answer in terms of the variables m, r, [tex]v_0[/tex], b, t, and c.

2. Relevant equations

[tex]a_{tan} = b + ct^2[/tex]

[tex]a_r=\tfrac{v^2}{r}[/tex]

Newton's Laws

3. The attempt at a solution

A. was not a problem for me:

[tex]F_{\tan}=ma_{\tan}=m(b+ct^2)[/tex]

For B.:

[tex]F_R=ma_r[/tex]

[tex]a_r=\tfrac{v^2}{r}[/tex]

It seems to make sense that because v is tangential speed we could use...

[tex]v(t)=v_0+a_{\tan}t=v_0+(b+ct^2)t[/tex]

So that...

[tex]a_r=\frac{(v_0+(b+ct^2)t)^2}{r}[/tex]

Finally giving...

[tex]F_R=m(\frac{(v_0+(b+ct^2)t)^2}{r}[/tex]

Which is not correct. What did I do wrong?

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

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: Non-uniform circular motion and tangential acceleration

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