# Rotational question

1. Apr 21, 2014

### bennyq

1. The problem statement, all variables and given/known data
The magnitude of the acceleration of a point on a spinning wheel is increased by a factor of 4 if:
A) the magnitues of the angular velocity and the angular acceleration are each multiplied by a factor of 4
B) the magnitues of the angular velocity is multuplied by a factor of 4 and the angular acceleration is not changed
C) the magnitues of the angular velocity and the angular acceleration are each multiplied by a factor of 2
D) the magnitues of the angular velocity is multiplied by a factor of 2 and the angular acceleration is not changed
E) the magnitues of the angular velocity is multiplied by a factor of 2 and the magnitudeof the angular acceleration is multiplied by a factor of 4

2. Relevant equations

3. The attempt at a solution

Okay i tried working back from this and must be doing something wrong,

and Atangential = rα

I rearange for A = Aradial + Atangentail (as vectors)

which is = r√α^2 + ω^4

subbing in 4 and 2 i get r√32

2. Apr 21, 2014

### Simon Bridge

You have interpreted "acceleration" in the question to mean the total acceleration.
For circular motion, radial acceleration ($\small{\ddot r}$) is zero - so you are summing the tangential and centripetal acceleration.

So $a=r\sqrt{\omega^4+\alpha^2}$

So far so good - but
...what did you put 4 nd 2 into and why?

Consider, multiplying angular velocity by 2 means that where you see a $\omega$ before, you put a $2\omega$.

Working in reverse is a good idea.
You need to put $a_{new}=4a=4r\sqrt{\omega^4+\alpha^2}$... work out how that 4 fits against the angular terms.

3. Apr 21, 2014

### Tanya Sharma

|a| = r√(α24) ,Now when you put αnew=4α and ωnew =2ω ,you get r√(16(α24)) = 4r√(α24)

Hence option E is correct.

4. Apr 21, 2014

### bennyq

ohhh of course.. thanks

5. Apr 21, 2014

### paisiello2

I think your mistake is that you are substituting values when you should be substituting in ratios.

6. Apr 21, 2014

### rude man

FINAL (I hope) EDIT:

I agree it's E.

Last edited: Apr 21, 2014