The problem reads: A cylindrical wheel (disk) of mass 10 kg andradius 0.5 meters

Question

The problem reads: A cylindrical wheel (disk) of mass 10 kg andradius 0.5 meters is released from rest while sitting on aninclined plane of inclination 30o.  The wheelis initially 5 meters (vertically). If the wheel rolls withoutslipping, what is its velocity when it reaches the bottom of theplane? ________m/s The problem reads: A cylindrical wheel (disk) of mass 10 kg andradius 0.5 meters is released from rest while sitting on aninclined plane of inclination 30o.  The wheelis initially 5 meters (vertically). If the wheel rolls withoutslipping, what is its velocity when it reaches the bottom of theplane? ________m/s

Explanation / Answer

    Mass of the wheel, M = 10 kg     Radius of the wheel, R = 0.5 m     Height, h = 5 m     Angle of inclined plane, = 30o     From law of conservation of energy,     ( KEt + KEr + PEg ) i = ( KEt + KEr +PEg ) f     Rotational Kinetic energy, KEr = ( 1/2 ) I2     0 + 0 + M g h = ( 1/2 ) M V2 + ( 1/2) ( M R 2 / 2 ) 2 + 0     But, V = R     M g h = ( 1/2 ) M V2 + ( 1/2 ) ( M V2 / 2 )     M g h = ( 1/2 ) M V2 ( 3 / 2 )     g h = ( 3 / 4 ) V 2     9.8 * 5 = 0.75 * V2     Velocity at the bottom, V = 8.1 m/s

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