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

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The problem involves calculating the net acceleration of a penny on a rotating disk, which starts from rest and has a constant angular acceleration of 1.9 rad/s². At t=1.2 seconds, the tangential acceleration is calculated as 2.66 m/s², while the radial acceleration is found to be 14.2644 m/s². However, there is confusion regarding the calculation of angular velocity, which should be expressed in rad/s rather than m/s; the correct angular velocity at t=1.2 seconds is 2.28 rad/s. The final net acceleration is derived from the combination of both tangential and radial accelerations, leading to a corrected value. Accurate unit representation and calculations are crucial for obtaining the correct answer.
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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The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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