July 5th, 2019, 04:41 AM  #11 
Math Team Joined: Jul 2011 From: Texas Posts: 2,980 Thanks: 1573  
July 8th, 2019, 07:52 AM  #12  
Senior Member Joined: Aug 2014 From: India Posts: 409 Thanks: 1  Quote:
 
July 8th, 2019, 02:27 PM  #13  
Math Team Joined: May 2013 From: The Astral plane Posts: 2,226 Thanks: 908 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
Dan  
July 8th, 2019, 11:00 PM  #14  
Senior Member Joined: Aug 2014 From: India Posts: 409 Thanks: 1  Quote:
Why $\displaystyle I \omega$ for spinning wheel and $\displaystyle mvr$ for clay? Clay is not symmetrical, so we have to use $\displaystyle mvr$ for it? Last edited by Ganesh Ujwal; July 8th, 2019 at 11:02 PM.  
July 9th, 2019, 01:44 AM  #15  
Math Team Joined: May 2013 From: The Astral plane Posts: 2,226 Thanks: 908 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
Though I was wrong about the clay not rotating the wheel, as it would roll away after the impact, the clay will simply not have enough momentum to make the wheel rotate with that amount of angular speed. The clay would have to hit the wheel at a different position to do that. (Basically momentum before = momentum after, so mv = (M + m)V, where M is the mass of the wheel and V the linear speed of the wheel and clay after collision. Then use the rolling without slipping condition $\displaystyle v = r \omega$.) Dan Addendum: For the clay, as stated in the problem, it really has not angular speed about the center of the wheel because it is coming in along the direction of a radius. (ie. the moment arm is 0). When it is stuck to the wheel we have $\displaystyle I_{clay} = mr^2$. Last edited by topsquark; July 9th, 2019 at 01:47 AM.  
July 9th, 2019, 06:03 AM  #16 
Senior Member Joined: Aug 2014 From: India Posts: 409 Thanks: 1  
July 9th, 2019, 02:50 PM  #17 
Global Moderator Joined: Dec 2006 Posts: 20,823 Thanks: 2160 
The problem states the wheel is set into pure rolling motion, which means no slipping. The wheel rotates about a moving axis, which is always its horizontal line of contact with the ground.


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