How Do You Calculate Accelerations and Distance in Gyroscope Dynamics?

AI Thread Summary
To calculate the tangential acceleration of a point on the rim of a gyroscope flywheel, use the formula a_t = r * α, where r is the radius and α is the angular acceleration. The radial acceleration at full speed can be found using a_r = ω² * r, where ω is the angular speed in radians per second. To determine the distance a point on the rim moves during the spin-up, apply the equation s = 0.5 * α * t², where t is the time taken to reach full speed. The discussion emphasizes understanding the relevant equations and encourages users to show their work for better assistance. Engaging with the problem-solving process is crucial for learning.
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A gyroscope flywheel of radius 3.33 cm is accelerated from rest at 13.4 rad/s2 until its angular speed is 2760 rev/min.
(a) What is the tangential acceleration of a point on the rim of the flywheel during this spin-up process?
m/s2
(b) What is the radial acceleration of this point when the flywheel is spinning at full speed?
m/s2
(c) Through what distance does a point on the rim move during the spin-up?
m

i've been trying to answer these for hours and still have no clue. Help is appreciated.
 
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