Question

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?

Answer 1

`32.7\ rad/sec^2`

Step-by-step explanation:

We have given the acceleration of the cord is
`3.27 m/sec^2` and acceleration due to gravity is
`9.81 m/sec^2` 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
`\alpha = (a)/(R)=(3.27)/(0.1)=32.7\ rad/sec^2` here α is angular acceleration a is linear acceleration and R is radius