# Conservation of energy; rotational kinetic energy

See attached file.

A cart consists of a body of mass M mounted on two uniform cylinders, each mass m, radius R. The cart is moving at velocity V at its initial location on a plane inclined at angle b. SEE ATTACHMENT #1 for a diagram showing parameters.

Known values are: M=2.1 kg, m=1.8 kg, angle b= 53 degrees, V= 2.5 m/sec.

PART a. Using conservation of energy, find the distance, D, that the cart moves up the plane in stopping.

PART b. Calculate what fraction of the initial total kinetic energy is rotational.

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#### Solution Preview

Recall that the rotational kinetic energy of an object is: (1) KErot= .5 I w^2 in which w is the angular velocity and i=.5 M R^2 is the moment of inertia about the c.m. axis.

Also, the linear velocity relates to the angular velocity by: (2) V= R w.

PART a.

Conservation of ...

#### Solution Summary

The solution shows the formulas and computations to arrive at the answers. The fraction of the initial total kinetic energy is rotational functions are determined.