Lab:�The Great �Toilet Paper �Drop Challenge

The Challenge

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Calculate the ratio of heights from which

a) a roll of toilet paper that is in free fall

and

b) a toilet paper roll whose end is being held and unrolls as it falls

must be dropped so that they hit the ground at the same time.

​

(In other words, H_freefall / h_unroll)

Materials

​

• two rolls of toilet paper
• meter stick
• electronic balance
• no internet!

Variables

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• m = mass
• R = outer radius of roll
• r = inner radius of roll
• F_P = force of unrolled toilet paper pulling upward on roll
• F_g = force of gravity

A Quick Lesson

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Remember Newton’s second law?

F_net = ma

​

There is an analogous rotational version! Any guesses?

τ_net = Iα

A Quick Lesson

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F_net = ma

The sum of the forces acting on the roll = m•a (translational motion)

​

τ_net = Iα

The sum of the torques acting on the roll = Iα

(rotational motion)

Assumptions

• The outer diameter change is negligible as the roll falls.
• Air resistance is negligible.
• The center of the roll is the center of mass.
• The masses of the rolls are the same (if not make them so)

Moments of Inetia