To prevent damage to her shoulders, your elderly grandmother wants to purchase t

Question

To prevent damage to her shoulders, your elderly grandmother wants to purchase the rug beater with the lowest moment of inertia about its grip end. Knowing you are taking physics, she asks your advice. There are two models to choose from. Model A has a 0.9-m-long handle on a 38.8-cm-edge-length square, where the masses of the handle and square are 1.1 kg and 0.6 kg, respectively. Model B has a 0.67-m-long handle and a 29.7-cm-edge-length square, where the masses of the handle and square are 1.30 kg and 0.7 kg, respectively.

Which model would you recommend?

Determine which beater is easier to swing from the very end by computing the moment of inertia for both beaters.

Explanation / Answer

Since moment of inertia is equal to mr2, we can solve the problem.

Model A - (1.1)(.45)2 + (.6)(1.094)2

Model A = .941 kgm2

Model B - (1.3)(.335)2 + (.7)(.8185)2

Model B = .615 kgm2

Model B is therefore easier to swing

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