Can This Thing Ever Happen?
A Uniform Disc Of Radius R And Mass m Is Projected Onto A Horizontal Floor With A Backward Spin Such That Its Centre Of Mass Speed Is v and Angular Velocity Is w . What Must Be The Minimum Value Of w So That The Disc Eventually Returns Back.
Details And Assumptions
Take Acceleration Due To Gravity = 10 SI Units
v = 10 m/sec
R = 5 m
The Ground Is Rough
If You Think That Situation Is Not Possible Then Give Your Answer As 0 .
Initial velocity of centre of mass is in forward direction
The answer is 4.
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1 solution
Notice such a situation can only arise When the velocity of the center of mass of the disc vanishes before it's angular velocity Using this as a base inequality And using force and torque equations we get Omega(minimum)=2v/R=4