What Power Is Needed To Accelerate An Object To 2.7 rad/s In 5.2 s?

AI Thread Summary
To determine the power needed to accelerate an object to an angular speed of 2.7 rad/s in 5.2 seconds, the relevant equation is P = W / t, where W represents work. The correct approach involves calculating the rotational kinetic energy (KE) at the target angular velocity, using the formula KE = 0.5 * I * ω², where I is the moment of inertia. The user initially struggled with finding acceleration and applied the wrong motion equation, leading to an incorrect result. Ultimately, the required power to achieve the desired acceleration is 1.3 W. Understanding the relationship between power, work, and kinetic energy is crucial for solving this problem.
n.hirsch1
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Homework Statement


See the image attached
What power must be applied to this object to accelerate it from rest to an angular speed of 2.7 rad/s in 5.2 s about the x axis?


Homework Equations


P = W / t - torque * angular velocity


The Attempt at a Solution


P = [(0.5 m)*(7 kg)*(acceleration)] * 2.7 rad/s
I don't know how to find acceleration or if I am doing this wrong all together. The right answer is 1.3 W. I tried plugging it into the motion equation v = vo + at to get a, that gave me the wrong answer.
 

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The work goes into making the system have kinetic energy. Your starting point should be P = KE/time. Now you just have to figure out how much rotational kinetic energy it has when ω = 2.7 rad/s.
 

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