Angular Velocity of Snow Ball

 

0.  Every year, when it snows a lot and my dad shovels the driveway, my mom told my sibling and I to help him out. Us helping him out clearing the driveway always ended up making us a snowman. The snowman that was made with clean snow that has not yet been affected by the dirt from the road and car was the best. As we gained more experience in making snowmen, one of the tricks we used was making a small ball of snow and rolling it down the hill, or any kind of surface that had a ramp. 

   
   

   Many snowballs that we rolled down the hill had both angular and linear velocity, which is why it was able to gain in size, especially on all sides, not just one side. If the snowball that was rolling down only had linear velocity and no angular velocity, the snowball would not get bigger in all sizes equally. 

   
   

   When I was rolling the snow down the hill, I felt like a bigger snowball was rolling down the hill faster although it was harder to carry them up the hill due to its heaviness. Today, I decided to look at the rotational kinetic energy of the snowball to see if it was because the heavier snowball had more kinetic energy. 

   
   
   

   

   For this case, I assumed that there is no work being done on the object. However, this is not necessarily true in real life. I assumed that the energy is conserved; therefore, as potential energy increases, kinetic energy increases. Since potential energy depends on the mass of the object, height, and gravity but height and gravity are held constant for two snowballs, kinetic energy solely depends on the mass of the snowball in this case. Using the equation for kinetic energy that accounts for both angular and linear motion, I was able to find the linear velocity of the snowball by using ‘dummy numbers’. To my surprise, the linear velocity of two snowballs was the same even though they had different mass and radius, in a world where there’s no friction. It led me to think about why I thought the heavier snowball was traveling faster in the beginning. It is because the angular velocity is different although linear velocity is the same! The angular velocity of the bigger snowball is calculated to be greater with 0.187 rad/s compared to the smaller snowball with 0.0374 rad/s. I must’ve thought that the bigger snowball was traveling faster than the smaller snowball since the bigger one had greater angular velocity. However, friction could have affected these two snowballs differently and that could lead to different results.