Physics questions???

Question

I know I have to use f= ma but im not exactly sure how and I need to study for a final.. Can someone please help??



A wheel of radius 27 cm, mass 3kg and moment of inertia 0.10935 kg m^2 is mounted on a frictionless, horizontal axle. A light cord wrapped around the wheel supports an object of mass 1.9 kg. The acceleration of gravity is 9.8 m/s^2. Find the tension T in the cord. Answer in units of N.


b) what is the angular acceleration of the wheel? answer in units of rad/s^2??

Answer 1

It is analogous in that torque=I*alpha

In this case you use both

The hanging mass has
m*a=m*g-tension

The wheel has
I*alpha=tension*r
so tension=I*alpha/r

plugging in
m*a=m*g-I*alpha/r

looks like two unknowns, but alpha can be relates to a as
alpha=a/r because the string is connected to the outer edge of the wheel
m*a=m*g-I*a/r^2
solving for a
a*(m+I/r^2)=m*g
a=m*g/(m+I/r^2)
calculate a and solve for tension using
m*a=m*g-tension
and check with
tension=I*a/r^2

b) is a/r or alpha

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