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# Physics/Rotational Problem

Question
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

Volunteer

#### Steve Johnson

##### Expertise

I would be delighted to help with questions up through the first year of college Physics. Particularly Electricity, Electronics and Newtonian Mechanics (motion, acceleration etc.). I decline questions on relativity and Atomic Physics. I also could discuss the Space Shuttle and space flight in general.

##### Experience

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
BS Physics, North Dakota State University
MS Electrical Engineering, North Dakota State University