How Do You Calculate Accelerations and Distance in Gyroscope Dynamics?

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SUMMARY

The discussion focuses on calculating the tangential and radial accelerations, as well as the distance traveled by a point on the rim of a gyroscope flywheel with a radius of 3.33 cm, which accelerates from rest at 13.4 rad/s² to an angular speed of 2760 rev/min. The tangential acceleration can be determined using the formula \( a_t = r \cdot \alpha \), where \( r \) is the radius and \( \alpha \) is the angular acceleration. The radial acceleration at full speed is calculated using \( a_r = \frac{v^2}{r} \), where \( v \) is the linear velocity derived from the angular speed. The distance traveled during the spin-up can be calculated using the kinematic equations for rotational motion.

PREREQUISITES
  • Understanding of angular acceleration and its relation to tangential acceleration
  • Familiarity with the conversion between angular speed in rev/min and linear velocity
  • Knowledge of kinematic equations for rotational motion
  • Basic proficiency in physics, specifically dynamics
NEXT STEPS
  • Calculate tangential acceleration using \( a_t = r \cdot \alpha \)
  • Determine radial acceleration at full speed with \( a_r = \frac{v^2}{r} \)
  • Explore kinematic equations for rotational motion to find distance traveled
  • Convert angular speed from rev/min to rad/s for accurate calculations
USEFUL FOR

Physics students, mechanical engineers, and anyone involved in dynamics and rotational motion calculations will benefit from this discussion.

rytagi17
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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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