Tangential and Normal of a rotating mass

[nysnacc]

Homework Statement

Homework Equations

a_t = Rα
a_n = V²/ R = Rω²

V_t Rω
V_n =0

The Attempt at a Solution

I found a_t=0
a_n=5.66 m/s
v_t=3.364
v_n=0

So v = v_t = 3.364 m/s[/B]
Correct?

 

[haruspex]

an=5.66 m/s

If you correct the units, yes.

vt=3.364

Please show how you got that.

 

[nysnacc]

oh yes, a in m/s^2 typo :)

for vt, first, I need ω, which is found from a_n = v^2/R where R is L sinθ

SO, v = sqrt (a_n*R) = sqrt (5.66*4sin30°) = 3.36 m/s

 

[gneill]

SO, v = sqrt (an*R) = sqrt (5.66*4sin30°) = 3.36 m/s

What are the units associated with that 4 (highlighted in red)?

 

[nysnacc]

4 in meter, which is the length of L

 

[nysnacc]

the question is modified, it was shown 4 ft but actually it should be in meter.

 

[gneill]

4 in meter, which is the length of L

the question is modified, it was shown 4 ft but actually it should be in meter.

Ah. It would have been nice to have been made aware of this detail in the problem statement

In that case your tangential velocity looks okay.

 

[nysnacc]

Hopefully I wouldn't make the same mistake next time, thanks for pointing out :)

And a_t = 0 (rotating in constant angular speed), v_n = 0 (constant radius R) correct?

 

[gneill]

And a_t = 0 (rotating in constant angular speed), v_n = 0 (constant radius R) correct?

Yes.

 

[nysnacc]

Yes.

Great! Actually these questions appeared on my midterm today, and these were my answers