A gyroscope flywheel of radius 1.93 cm is accelerated from rest at 14.3 rad/s2 u

Question

A gyroscope flywheel of radius 1.93 cm is accelerated from rest at 14.3 rad/s2 until its angular speed is 1540 rev/min. (a) What is the tangential acceleration of a point on the rim of the flywheel during this spin-up process? (b) What is the radial acceleration of this point when the flywheel is spinning at full speed? (c) Through what distance does a point on the rim move during the spin-up? A gyroscope flywheel of radius 1.93 cm is accelerated from rest at 14.3 rad/s2 until its angular speed is 1540 rev/min. (a) What is the tangential acceleration of a point on the rim of the flywheel during this spin-up process? (b) What is the radial acceleration of this point when the flywheel is spinning at full speed? (c) Through what distance does a point on the rim move during the spin-up? A gyroscope flywheel of radius 1.93 cm is accelerated from rest at 14.3 rad/s2 until its angular speed is 1540 rev/min. (a) What is the tangential acceleration of a point on the rim of the flywheel during this spin-up process? (b) What is the radial acceleration of this point when the flywheel is spinning at full speed? (c) Through what distance does a point on the rim move during the spin-up?

Explanation / Answer

A) radius of the wheel is r = 1.93 cm = 0.0193 m

angular acceration alpha= 14.3 rad/s^2

tangential accelaration atan = r*alpha = 0.0193*14.3 = 0.27599 m/s^2

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B) angular speed is w = 1540*2*3.142/60 = 161.3 rad/s

radial accelaration arad = r*w^2 = 0.0193*161.3^2 = 502.1 m/s^2

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C) time taken t = 161.3/14.3 = 11.3 S

distance moved is s = 0.5*a*t^2 = 0.5*0.27599*11.3*11.3 = 17.62 m

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