What Factors Increase the Acceleration on a Spinning Wheel?

[bennyq]

Homework Statement

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

answer is E

Homework Equations

The Attempt at a Solution

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

I start with Aradial = v^2/r = rω^2
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

 

[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

subbing in 4 and 2 i get r√32

...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.

 

[Tanya Sharma]

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

I start with Aradial = v^2/r = rω^2
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

|a| = r√(α²+ω⁴) ,Now when you put α_new=4α and ω_new =2ω ,you get r√(16(α²+ω⁴)) = 4r√(α²+ω⁴)

Hence option E is correct.

 

[bennyq]

ohhh of course.. thanks

 

[paisiello2]

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

 

[rude man]

FINAL (I hope) EDIT:

I agree it's E.