A bucket holding a cartoon character is dangling from a rope above a well from the windlass which raises the bucket from the well. The bucket and character have a combined mass of 10.0 kg. The distracted friend lets go of the handle, and the bucket falls, unwinding the windlass. The acceleration of the character and bucket is 4.9 m/s2. The windlass has a radius of 0.20 meters. What is the moment of inertia of the windlass

Question

Marquez

Physics

14 May, 23:44

A bucket holding a cartoon character is dangling from a rope above a well from the windlass which raises the bucket from the well. The bucket and character have a combined mass of 10.0 kg. The distracted friend lets go of the handle, and the bucket falls, unwinding the windlass. The acceleration of the character and bucket is 4.9 m/s2. The windlass has a radius of 0.20 meters. What is the moment of inertia of the windlass

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Porter Mendoza · Answer 1

I = 0.4 kg m²

Explanation:

Let's solve this exercise in part, let's first work with the cube.

W - T = m a

T = W - m a

T = m (g-a)

T = 10.0 (9.8 - 4.9)

T = 49 N

Now let's work on the pinwheel, we write Newton's rotational law

τ = I α

T r = I α

Linear and angular variables are related.

a = α r

α = a / r

We replace

T r = I a / r

I = T r² / a

we calculate

I = 49 0.20² / 4.9

I = 0.4 kg m²