Force F = ─10ĵ N is exerted on a particle at 𝓇 = (5î＋5ĵ) m. What is the torque on the particle about the origin?

Video transcript

Hi, everyone in this practice problem, we're being asked to find the porque produced by a force. We will have a sphere placed in the frame at the position of 1.5 m comma 2.5 m comma zero. And it's going to be subjected to a force which follow the equation of F equals negative three I Newton. And we're being asked to find the torque produced by F about the point of origin or 0.0.0 or 0.0 comma zero comma zero. The options given are a negative 4.5 I Newton meter B 4.0 J. Newton meter C 7.5 J Newton meter and lastly D 7.5 K Newton meter. So by definition, torque is going to equal to the cross product of the position factor from the axis of rotation to the point of application of the force. And the force factor or essentially tau will equals to R crossed. The position factor given is going to be R equals to 1.5 I plus 2.5 J and all of that is going to be in meter. The force is given by F equals negative three I Newton. So we wanna apply equation one with this two R and F to obtain the torque produced by F above the point of origin. So then we will have pork to equals to R cross F which will equals to the R is going to be 1.5 I uh plus 2.5 J cross that with negative three I and we will get all of this in Newton meter just like so and then simplifying or actually doing the cross product, then Tau will equals to 1.5 multiplied by negative three I cross eye plus 2. multiplied by negative three J cross I. This is going to be in Newton meter again. So if we recall, I crossed I well equals to zero while J cross, I will actually equals to negative K just like so, so uh using this uh knowledge right here, we can then cross out the first part of our torque because it will equals to zero because I cross I will equals to zero. And then the second part will then govern us to to be equals to 2.5 times negative three is going to be negative 7.5 and J cross I is going to be negative K and all that is going to be in Newton meter. So then our torque will then equals to 7.5 K Newton meter just like. So, so the talk produced by F on the sphere about the point of origin or 0.0.0 equals zero. Comma zero, comma zero will be 7.5 K Newton meter, which will correspond to option D in our answer choices. So option D will be the answer to this particular practice problem. And that'll be it for this video. If you guys still have any sort of confusion, please make sure to check out our adolescent videos on similar topics and that'll be it for this one. Thank you.