# Conservation of Energy in Rolling Motion - Video Tutorials & Practice Problems

## Conservation of Energy in Rolling Motion

A solid sphere of mass M = 10 kg and radius R = 2 is rolling without slipping with speed V = 5 m/s on a flat surface when it reaches the bottom of an inclined plane that makes an angle of Θ = 37° with the horizontal. The plane has just enough friction to cause the sphere to roll without slipping while going up. What maximum height will the sphere attain? (Use *g* = 10 m/s^{2}.)

## Sphere on rough and smooth hills

You may remember that the lowest speed that an object may have at the top of a loop-the-loop of radius R, so that it completes the loop without falling, is √gR . Determine the lowest speed that a solid sphere must have at the bottom of a loop-the-loop, so that it reaches the top with enough speed to complete the loop. Assume the sphere rolls without slipping.

$\sqrt{5gR}$

$\sqrt{\frac{13gR}{5}}$

$\sqrt{\frac{27gR}{7}}$

$\sqrt{10gR}$

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