A small, solid cylinder with mass = 20 kg and radius = 0.10 m starts from rest and rotates without friction about a fixed axis through its center of mass. A string is wrapped around the circumference of the cylinder and pulled using a constant force F. The resulting angular acceleration of the cylinder is 5.0 rad/s2. What length of string has unwound after 4.0 s, in meters? (The moment of inertia of the cylinder is 1 half M R squared.)

Question

Danica Ferrell

Physics

22 October, 05:10

A small, solid cylinder with mass = 20 kg and radius = 0.10 m starts from rest and rotates without friction about a fixed axis through its center of mass. A string is wrapped around the circumference of the cylinder and pulled using a constant force F. The resulting angular acceleration of the cylinder is 5.0 rad/s2. What length of string has unwound after 4.0 s, in meters? (The moment of inertia of the cylinder is 1 half M R squared.)

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Beau Terrell · Answer 1

angular acceleration α = 5 rad / s ²

θ = 1/2 α t², θ is angle of rotation, t is time.

=.5 x 5 x 4²

= 40 rad.

θ = l / r, θ is angle formed, l is length unwound, r is radius o wheel.

l = θ x r

= 40 x. 1

= 4 m.