How large torque is needed for acceleration

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To calculate the torque needed to accelerate a disk with a radius of 2 cm and mass of 2 kg from rest to 60 rad/s in 6 seconds, one must first determine the moment of inertia of the disk, which is 0.5 * mass * radius^2. The angular acceleration can be found by dividing the change in angular velocity by the time taken. Once the angular acceleration is known, torque can be calculated using the formula torque = moment of inertia * angular acceleration. Providing a detailed attempt at the solution, including relevant equations, is essential for receiving effective assistance. Engaging with the problem will enhance understanding and facilitate learning.
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Hi! I am trying to solve a physics task, but can't get it right. Would really appreciate some help..

A disk of uniform thickness has a radius of 2cm and the mass of 2kg. How large torque is needed to accelerate it from the rest up to 60 rad/s in 6seconds?
 
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What he said. You said you can't get it right which implies you have at least had a go. Tell us what you did and we can help you find the error. This approach helps you learn and saves us having to repeat stuff you already know.
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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