Solid sphere rolling down a house roof.... angular speed

[shmoop]

Homework Statement

A solid sphere of radius 16cm and mass 10kg starts from rest and rolls without slipping a distance of 9m down a house roof that is inclined at 43 degrees.

What is the angular speed about its center as it leaves the house roof?

The height of the outside wall of the house is 6m. What is the horizontal displacement of the sphere between the time in which it leaves the roof and the time at which it hits the ground?

Homework Equations

Torque=Inertia*Angular Acceleration (?)

Inertia of a solid sphere =0.4*m*r^2

I'm not really sure.. but:

Vf^2=Vo^2+2ad

The Attempt at a Solution

Inertia of the sphere.. incase I need it?
I=0.4*10kg*0.16m^2= 0.1024 kg*m^2

Viy= 0m/s
Vfy= ?
Ay= -9.8m/s^2
delta y= 9sin43= -6.1379m (vertical displacement)

Then I tried to calculate for the final vertical velocity (before it rolls off the roof)
Vfy^2=Viy^2+2ady

Vfy= sqrt(2*-9.8m/s^2*-6.1379m)

Vfy= 10.968 m/s

Then I tried to calculate for the final velocity before the ball rolls off the roof:
Vf= 10.968/sin43 = 16.0821

Then I tried to convert it to angular velocity:
V=r*ω
ω=V/r
ω=16.0821m/s / 0.16m = 100.5 rad/sI know this is incorrect, but I'm unsure as to where I went wrong. I'm trying to solve the problem without using work/energy, as my teacher hasn't yet covered those topics. If someone could point me in the right direction it would be GREATLY appreciated! Thanks :)

 

[BvU]

Hi,

Did you make a sketch of the various forces that accelerate/slow down the ball ?

Ay= -9.8m/s^2

No. See your drawing. And use subscripts.

rolls without slipping

Where do you use that ?
Where do you use $\tau = I\alpha$ ?

Vfy^2=Viy^2+2ady

Who is ady ? Use only variables you have explained. Don't use A and a to denote the same variable.

 

[rude man]

Basic hint: sum of kinetic energies due to distance traveled by the c.g. plus rotational kinetic energy = total loss of potential energy.