Question

A coin is placed on a horizontal table rotating at 33.3 rpm revolves with the table without slipping, provided the coin is not more than 0.1 m away from the axis. How far from the axis can the coin be placed so that it revolves with the table without slipping if the turn table rotates at 45 rpm

Answer 1

ANSWER

When the coin is just on the verge of slipping, it just overcomes the force of static friction (F  

s

​  

) . which acts as centripetal force for being that coin in the circular motion.

So we have

F  

s

​  

=mω  

2

r

If we double the ω,  then r will also self adjust to a new r  

′

 

, since the static friction will remain same. We have

mω  

2

r=m(2ω)  

2

r  

′

 

 

⇒r  

′

 

=  

4

r

​  

 cm=  

4

4

​  

 cm=1 cm