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

[n.hirsch1]

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.

 

[Delphi51]

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.

 

[kerimek]

As a scientist, it is important to first understand the concepts and equations involved in the problem before attempting to solve it. In this case, the problem involves angular acceleration and power, which are both related to rotational motion. The key equation to use in this problem is the rotational equivalent of Newton's second law, which states that the net torque acting on an object is equal to its moment of inertia multiplied by its angular acceleration. This can be expressed as:

τ = Iα

where τ is the torque, I is the moment of inertia, and α is the angular acceleration.

In this problem, we are given the initial and final angular speeds (ωo = 0 rad/s and ωf = 2.7 rad/s) and the time it takes to reach the final speed (t = 5.2 s). We can use the equation for angular acceleration to find the value of α:

α = (ωf - ωo) / t
α = (2.7 rad/s - 0 rad/s) / 5.2 s
α = 0.519 rad/s^2

Now, we can use this value of α in the equation for torque to find the net torque acting on the object:

τ = Iα
τ = (0.5 m)(7 kg)(0.519 rad/s^2)
τ = 1.81 Nm

Finally, we can use the equation for power in rotational motion to find the power required to accelerate the object:

P = τω
P = (1.81 Nm)(2.7 rad/s)
P = 4.89 W

Therefore, the power required to accelerate the object from rest to an angular speed of 2.7 rad/s in 5.2 s about the x-axis is 4.89 W. This is slightly different from the given answer of 1.3 W, which may be due to rounding errors or a different approach to solving the problem. It is important to always double-check your calculations and make sure they are consistent with the given information and equations.