What is the net acceleration of the coin on a rotating disk?

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SUMMARY

The net acceleration of a coin on a rotating disk can be calculated using both tangential and radial acceleration components. In this scenario, a disk with a constant angular acceleration of 1.9 rad/s² rotates around a fixed vertical axis. At t=1.2 seconds, the tangential acceleration is determined to be 2.66 m/s², while the angular velocity is correctly calculated as 2.28 rad/s. The radial acceleration is then computed as 14.2644 m/s², leading to a total net acceleration of 14.51 m/s² when combining both components.

PREREQUISITES
  • Understanding of angular acceleration and its effects on linear motion
  • Familiarity with the equations of motion for rotational dynamics
  • Knowledge of tangential and radial acceleration calculations
  • Ability to differentiate between angular velocity and tangential velocity
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  • Study the relationship between angular acceleration and tangential acceleration in rotational systems
  • Learn how to calculate radial acceleration using angular velocity
  • Explore the concept of net acceleration in circular motion
  • Review the differences between linear and angular motion equations
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ComputerForests000
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Homework Statement


A disk is initially at rest. A penny is placed on it at a distance of 1.4 m from the rotation axis. At time t=0s, the disk begins to rotate with a constant angular acceleration of 1.9 rad/s^2 around a fixed, vertical axis through it's center and perpendicular to it's plane. Find the magnitude of the net acceleration of the coin at t=1.2 seconds.

Homework Equations


tangential acceleration=α r
radial acceleration= r ω^2
ω = ω initial + α t

The Attempt at a Solution


I found the tangential acceleration to be 2.66 m/s^2,
then used ω = ω initial + α t to find the angular velocity, 3.192 m/s,
then found the radial acceleration to be 14.2644 m/s^2,
then took the square root of (tangential acceleration)^2 +(radial acceleration)^2 , which came out to be:
14.51 m/s^2
Apparently this answer is incorrect.
 
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Something is wrong with the calculation of angular velocity (you also report it in units m/s which is also wrong), I calculated that is equal to 2.28 rad/s at time t=1.2s.
 
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ComputerForests000 said:
to find the angular velocity, 3.192 m/s,
That's the tangential velocity, not the angular velocity.
 
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