A ball filled with an unknown material starts from rest at the top of a 2 m high incline that makes a 28o with respect to the horizontal. The ball rolls without slipping down the incline and at the bottom has a speed of 4.9 m/s. How many revolutions does the ball rotate through as it rolls down the incline

Searching in google I found the total mass and the radius of the ball (m = 1.5 kg and r = 10 cm) which are needed to solve the problem!  

The ball rotates 6.78 revolutions.

Explanation:

Searching in google I found the total mass and the radius of the ball (m = 1.5 kg and r = 10 cm) which are needed to solve the problem!        

At the bottom the ball has the following angular speed:

Now, we need to find the distance traveled by the ball (L) by using θ=28° and h(height) = 2 m:

To find the revolutions we need the time, which can be found using the following equation:                

(1)

So first, we need to find the acceleration:

   (2)  

By entering equation (2) into (1) we have:

Since it starts from rest (v₀ = 0):  

Finally, we can find the revolutions:  

Therefore, the ball rotates 6.78 revolutions.

I hope it helps you!