Torque and angular acceleration pulley problem

[BrainMan]

Homework Statement

A pulley in the shape of a cylinder of mass 5 kg and radius 0.6 m has a force of magnitude 30 N exerted tangentially on it. Find the angular acceleration of the pulley and its angular velocity after 3 s, assuming it starts from rest.

Homework Equations

T = Ftr
T = mr^2a

The Attempt at a Solution

(a) I tried to find the acceleration using torque equations
T = FtR
T = 30(.6)
T=18

T = mr^2a
18 = 5(.36)a
a = 10 rad/sec^2

(b) Then I took the acceleration and tried to find the angular velocity
ω = ω_i + at
ω = 10(3)
ω = 30 rad/sec

They correct answer is (a) 20 rad/sec^2 (b) 60 rad/sec

 

[Tanya Sharma]

T = mr^2a
18 = 5(.36)a
a = 10 rad/sec^2

You have used MI of a hollow cylinder whereas pulley is a solid cylinder .Use Moment of inertia of solid cylinder .

 

[BrainMan]

You have used MI of a hollow cylinder whereas pulley is a solid cylinder .Use Moment of inertia of solid cylinder .

I got it right. Thanks!