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Suppose you roll a disk up a slope with an initial velocity v=17m/s at a 33 degree angle. When will it come to rest?

Hello Rod,

Use conservation of energy. When it comes to a stop, 100% of the original kinetic energy will have converted to gravitational potential energy. Let the mass be m, the radius be r, and d be the distance up the slope.

Initial linear kinetic energy:

(1/2)*m*v^2

Initial angular kinetic energy:

(1/2)*I*w^2

where I = m*r^2/2 and w = v/r -- so this becomes (1/2)*m*v^2 + (1/4)*m*v^2

Final gravitational potential energy

m*g*y

where y = d*sin33 -- so this is m*g*d*sin33

Due to conservation of energy,

(3/4)*m*v^2 = m*g*d*sin33

Solve for d. So it's when it has gone the distance d.

I hope this helps,

Steve

Physics

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I have a BS in Physics and an MS in Electrical Engineering. I am retired now. My professional career was in Electrical Engineering with considerable time spent working with accelerometers, gyroscopes and flight dynamics (Physics related topics) while working on the Space Shuttle. I gave formal classroom lessons to technical co-workers periodically over a several year period.**Education/Credentials**

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