Types of Acceleration in Rotation Video Lessons

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Problem: A rotating platform of radius R = 4.5 cm starts from rest and accelerates with uniform angular acceleration α = 42 rad/s2.Part (a). Write an expression that gives the centripetal acceleration on the edge of the platform as a function of time ac(t).Part (b). Write an expression for the time at which the magnitudes of the centripetal and tangential accelerations at the edge will be equal. Part (c). Calculate the time, in seconds, for when the magnitudes of the centripetal and tangential accelerations are equal.

FREE Expert Solution

Rotational kinematic equations:

ωf=ω0 + αtθ=12(ω0+ωf)tθ=ω0t +12αt2ωf2=ω02+2αθ

(a)

Centripetal acceleration:

ac=v2r=rω2

Using the first rotational kinematic equation:

ω(t) = ω0 + αt

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Problem Details

A rotating platform of radius R = 4.5 cm starts from rest and accelerates with uniform angular acceleration α = 42 rad/s2.

Part (a). Write an expression that gives the centripetal acceleration on the edge of the platform as a function of time ac(t).

Part (b). Write an expression for the time at which the magnitudes of the centripetal and tangential accelerations at the edge will be equal.

 Part (c). Calculate the time, in seconds, for when the magnitudes of the centripetal and tangential accelerations are equal.

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