What Is the Correct Translational Velocity of a Disk Rolling Down an Incline?

AI Thread Summary
The problem involves calculating the translational velocity of a disk rolling down an incline from a height of 15 meters. The moment of inertia for the disk is given as I=1/2MR², and the relevant equations include potential energy (PE) and kinetic energy (KE). The correct approach requires incorporating both translational and rotational kinetic energy into the calculations. By substituting the moment of inertia and angular velocity into the kinetic energy equation, one can derive the final velocity. The solution emphasizes the importance of considering rotational dynamics in addition to translational motion.
alexito01
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Homework Statement


A disk is released from rest from the top of an incline. The bottom of the incline is a vertical distance h=15m below the top. The wheel rolls without slipping. The moment of inertia of the disk is given by I=1/2MR2. What is the translational velocity of the disk at the bottom of the incline? (use g=9.8m/s2)


Homework Equations


PE= mgy and KE= 1/2mv^2 and ω=v/r


The Attempt at a Solution


I ended up with 17.1 m/s but it keeps telling me its wrong
 
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Are you using rotational kinetic energy anywhere in your calculations? Notice that you were given the moment of inertia of a disk.
 
Ki = 0
Kf = translation kinetic energy + rotational kinetic energy = 1/2 Mv^2 + 1/2 I w^2
In the above, substitute I = 1/2 MR^2 and w = v/R to find Kf in terms of M and v.

Ui = Mgy
Uf = 0
Kf + Uf = Ki + Ui
Substitute values and solve for v.
 
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