Question

You and a friend are playing with a Coke can that you froze so it's solid to demonstrate some ideas of Rotational Physics. First, though, you want to calculate the Rotational Kinetic Energy of the can as it rolls down a sidewalk without slipping. This means it has both linear kinetic energy and rotational kinetic energy. [The freezing only matters because if there is liquid inside, the calculation for the Moment of inertia becomes more complicated]. A Coke can can be modeled as a solid cylinder rotating about its axis through the center of the cylinder. This can has a mass of 0.33 kg and a radius of 3.20 cm. You'll need to look up the equation for the Moment of Inertia in your textbook. It is rotating with a linear velocity of 6.00 meters / second in the counter-clockwise (or positive) direction. You can use this to determine the angular velocity of the can (since it is rolling without slipping). What is the Total Kinetic Energy of the Coke can

Answer 1

K_{total} = 8.91 J

Step-by-step explanation:

In this exercise you are asked to find the kinetic energy of the can of coca-cola

K_total = K_ {Translation} + K_ {rotation}

the translational kinetic energy is

K_ {translation} = ½ m v²

the kinetic energy of rotation is

K_ {rotation} = ½ I w²

The moment of inertia of a cylinder is

I = ½ m r²

we substitute

K_ {total} = ½ m v² + ½ (½ m r²) w²

angular and linear velocity are related

v = w r

we substitute

K_ {total} = ½ m v² + ¼ m r² v² / r²

K_ {total} = m v² (½ + ¼)

K_ {total} = ¾ m v²

let's calculate

K_ {total} = ¾ 0.33 6.00²

K_{total} = 8.91 J