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Please help me with the sum : A ring of radius R rolls on a horizontal ground with linear speed v and angular speed ω = 2v/ R . Let there be a point P on the rim of the ring such that it makes an angle θ with the center of the the ring , for what value of θ the velocity of point P will be in vertical upward direction.

Please help me with the sum :
 
A ring of radius R rolls on a horizontal ground with linear speed v and angular speed ω = 2v/R . Let there be a point P on the rim of the ring such that it makes an angle θ with the center of the the ring , for what value of θ the velocity of point P will be in vertical upward direction.

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Grade:11

1 Answers

Arun
25750 Points
5 years ago
its 60degrees, coz 
split the velocities into linear and angular velocity. 
now the linear velocity for all the points on the ring is same in magnitude(=V) and direction(HORIZONTAL) 
while angular velocity has constant mag(=2v/R) but the direction varies with the position of point P. 
the now consider the ring is just rotating and try to fix point P at a position where its component along the horizontal is of mag. v and is opposite in direction to the linear velocity. 

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