An object's moment of inertia is 2.0 kg m^2. Its angular velocity is increasing at the rate of 4.0 rad/s per second. What is the net torque on the object?

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Hey, everyone in this problem, the motor of a handheld sander machine applies a steady torque tow to the disc enhancing its angular velocity by 1. radiance per second. Each second, the moment of inertia of the disk is three kg meters squared. And we are asked to calculate the torque tow. We're given four answer choices. All four of them have the unit of Newton meters. Option A is 0.5. Option B is two, option C is 4.5 and option D is 6.8. Now we're asked to calculate the torque and let's recall that the sum of the torques is equal to I alpha where I is the moment of inertia and alpha is the angular acceleration. Now, we're given the moment of inertia of the disc three kg meters squared. OK. So we have I and what do we know about alpha? We're told that the angular velocity is going to enhance by 1.5 radiance per second each second. What that tells us is that our angular acceleration is actually 1.5 radiance per second squared. And because our velocity is increasing by 1.5 radiance per second, every second, 1.5 ratings per second squared. Ok. All right. So we actually have both alpha and I. Ok. Again, I is three kg meters squared. So we have everything we need to calculate this torque, we just need to summon these values and solve. Ok. So our moment of inertia, I three kg meter squared multiplied by the angular acceleration 1. radiance per second squared, which gives us a torque towel of 4. Newton meters. OK? We had kilogram meter squared per second squared. Recall that a Newton is equivalent to a kilogram meter per second squared. And so kilogram meter squared per second squared is equivalent to a Newton meter and that's it for this problem. OK. Our torque tow is gonna be 4.5 Newton meters which corresponds with answer choice. C Thanks everyone for watching. I hope this video helped see you in the next one.

An object's moment of inertia is 2.0 kg m^2. Its angular velocity is increasing at the rate of 4.0 rad/s per second. What is the net torque on the object?

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Key Concepts

Moment of Inertia

Angular Acceleration

Torque