Linear and angular acceleration problems.

jeudi 29 août 2013

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.