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A uniform disk of unknown mass M and radius R = 10 cm is free to rotate about its axis. A light cord is wrapped around the rim on the disk and then tied to a small can of mass m = 50 gm. The cord does not slip as it unwinds on the disk. When released the can moves down with acceleration 3.27 m/s2. Take g = 9.81 m/s2. What is the angular acceleration of the disk?

Respuesta :

Answer:

[tex]32.7\ rad/sec^2[/tex]

Explanation:

We have given the acceleration of the cord is [tex]3.27 m/sec^2[/tex] and acceleration due to gravity is [tex]9.81 m/sec^2[/tex] there is a relation between the angular acceleration and the linear acceleration that is

Linear acceleration = angular acceleration × radius

We have given radius R = 10 cm =0.1 m

So [tex]\alpha = \frac{a}{R}=\frac{3.27}{0.1}=32.7\ rad/sec^2[/tex] here α is angular acceleration a is linear acceleration and R is radius