# Linear and angular acceleration problems.

1. Aug 29, 2013

### brenfox

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

A mass of 0.5kg is suspended from a flywheel. If the mass is released from rest and falls a distance of 0.5m in 1.5s. ( mass of wheel = 3kg, Radius = 0.3m, Radius of gyration = 212mm ).

Calculate : a:The linear acceleration of the mass?
b: The angular acceleration of the wheel?

2. Relevant equations

v=s/t
a= v-u/t
s=ut+1/2at^2

3. The attempt at a solution

I am getting conflicting answers to these questions. Heres my attempt!
v = s/t so... v = 0.5/1.5 = 0.3333ms-1.
Then...
a = v-u/t so... v = 0.3333 - 0/1.5 = 0.2222ms-2

So linear acceleration = 0.2222ms-2

Question b : angular acceleration = acceleration/radius.

so...

angular acceleration = 0.2222/ 0.3 = 0.74 Rads-2.

Now my linear acceleration is 0.222ms-2

so if i put this answer into the equation s = ut + 1/2at^2. s should equal 0.5m. so..

s = 1.5+1/2X0.2222x1.5^2 = 1.75s??? The answer should be 0.5m?

Any help will be greatfully accepted.

2. Aug 29, 2013

### LeonhardEu

In your first equation you have not considered that there is acceleration so v is not s/t

Edit: Also you have not considered that it begins from REST and falls 0.5m in 1.5s

3. Aug 29, 2013

### brenfox

Average velocity = 0.5/1.5 = 0.3333ms

So the distance from rest to fall = 0.5m so...

0.333/0.5 = 0.6666ms.

So velocity increases from 0 to 0.666ms in 1.5s.

then: a= 0.6666/1.5 = 0.444ms-2 is the linear acceleration????

4. Aug 29, 2013

### LeonhardEu

No. You have acceleration so
v = at
s = 0.5at^2 are your equations

5. Aug 29, 2013

### brenfox

third time lucky

v = at

a = v/t

a = 0.3333/1.5 = 0.2222ms-1

a = 0.2222ms-1 but distance is 0.5m so:

0.2222/0.5 = 0.4444ms-2

linear acceleration = 0.4444ms-2.

checking with equation s = 0.5at^2

s = 0.5x0.444x1.5^2 = 0.5m

so inserting 0.4444 into the above equation gives me the correct distance. To my knowledge this tells me 0.4444ms-2 is correct??

6. Aug 29, 2013

### CAF123

7. Aug 29, 2013

### LeonhardEu

Well done. I think you are on your start doing physics. Try making good shapes and for every body you study draw the forces upon it so you can see how it will react. ;)

8. Aug 29, 2013

so