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Two identical 4-lb slender rods $A B$ and $B C$ a…

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Problem 87 Easy Difficulty

A $4-\mathrm{kg}$ slender rod is welded to the edge of a $3-\mathrm{kg}$ uniform disk as shown. The assembly rotates about $A$ in a vertical plane under the combined effect of gravity and of the vertical force $\mathbf{P}$. Knowing that at the instant shown the assembly has an angular velocity of $12 \mathrm{rad} / \mathrm{s}$ and an angular acceleration of $36 \mathrm{rad} / \mathrm{s}^{2},$ both counterclockwise, deter mine $(a)$ the force $\mathbf{P},(b)$ the components of the reaction at $A$

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Video Transcript

hello friends As surrender figure, there is a risk off must nine kg and already it's 200 millimeters that is find committed it attached to the sledder or a B off Must The Mars off rod is given right on the length off Rod is given 500 millimeters, that is, find 5 m. There are two points be and she bitch are fiction. Let's assembly rotates in a vertical plane under combined effective gravity and couple M, which is applied to a rod A V. It is given that assembly having Ang Global City six million per second on angular acceleration off 25 Radian per second square when a couple damage applied. So then couple M is applied at that instant. It's angular. Velocity is six radian per second on angular acceleration is 25 a radiant per second square. We have to calculate West Park. The couple m applied second reactions by the pain seat on Rod Evie. The reaction off. See, we have to calculate that is the start solving it. First, we will calculate moment Orphanage of the Rod about X geometrical center or center off months. This would be won by 12 top um are in tow Square off, let off rod length, off road. You may call length off every more precisely. And this is the mass off baby. So be careful. Substituting developed mass off road A B is given five pg and its length is quite 5 m. So moment off Energia about its geometrical center would be why one euro for what six of it give me to respect Yeah. On moment off, Inertia off disc about center off. Must is half moss MD in tow. Previous off this square substituting the Palomas off. This case, given nine cages on its radius, is going to so moment. Often it's of the disc about this is center off mass perpendicular to its place will be 0.18 k g. Meter square, angular. Excellent story. Acceleration of the rod will be 0.25 and Tau Alpha using is called toe Alpine tour. And that off this kid will be Why fight in to help us? Let us hear off free body diagram off the system here I will. So, all the forces acting on the system at the point there is a weight off the disk at the midpoint off a V. There is a weight off the road. This is a couple applied on it. This is a geometrical center or center off most of the road. So here it will experience acceleration force due to acceleration, normal and Tunisia. And along this direction, I'm marking with blue collar must off road and tow normal reaction on the road. This distance will be 0.25 and this would be also 1 to 5 needed here. Edible experience. I into ALPA despicable experience and initial foods into tenure Ship ID in tow. Alfa and one more force will act on the disk. That is, I'm marking here most off the disk and tow normal reaction. Let us start solving it. That's a spark finding the couple about the 0.8. Yes, you will get em minus couple due to the weight of the rod. About the 0.8 couple do toe. Wait off the disk about the point a forced into perpendicular distance. And that will be moment off inertia into angular acceleration off the road and are a RT into 1 to 5 less moment off the disk into angular acceleration mass of the disk into. It's a 10 initial acceleration and took quite place subject to bring the value must off road is given nine kg nine in 29.81 and 2.5. This is the weight off the road. Wait off the disk is given five kg. Sorry. Bait off the road is given five g and that off Biscuit 90. Yeah, moment off ownership the road. Already we have calculated why 10 or one, 67 and two Alfa on angular acceleration is given or in the last people substitute. After doing all the calculation in the right hand side, that will be easier. 15 and 2.25 Alfa and find 25 plus find 18 into a farm moment off energy off that this last nine in 2.54 and 2.5. So in the right inside we can write. After solving these two terms, you will get 28.0 food 2.8467 and Tau Alpha on Alfa is given to us 25 radiant per second square. So from here, couple acting on the system is 99.4 Newton meter in contract blocked by direction. So this is the answer off part eight. Now we have to calculate the reactions at sea point. Be part we're solving. We will analyze on little forces acting on the disk, not the complete assembly. This is the disk. No. Be point see point. Suppose if the reaction is here it having the reaction BX and or gentle direction on reaction B Y in the vertical direction. Or you may draw like this. This is the point on it. There will be attending initial foods on it, having the normal force and force you to rotation now calculating couple about the point. And here the bait off the disk collect. Yeah. So calculating the couple about the three point and taking contract. Rock bites. Toby Positive. We will get see in 2.15 It's called ID into Elba. Moment off. In itself, that disk about extra center is quite one. It on angular acceleration is 25 so he will be 30.0 new 10 m. 30 30 point. You know Newton. That's all for it. Thanks for watching it

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Problem

Two identical 4-lb slender rods $A B$ and $B C$ a…

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Related Courses

Vector Mechanics for Engineers: Statics and Dynamics

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Video Transcript

Ferdinand P. Beer, E. Russell Johnston, Jr., David F. Mazurek

Vector Mechanics for Engineers: Statics and Dynamics

Elyse Gonzalez

Christina Krawiec

Marshall Styczinski

Farnaz Mohseni

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Vector Mechanics for Engineers: Statics and Dynamics

Elyse Gonzalez

Christina Krawiec

Marshall Styczinski

Farnaz Mohseni

Ferdinand P. Beer, E. Russell Johnston, Jr., David F. Mazurek Vector Mechanics for Engineers: Statics and Dynamics

Elyse Gonzalez

Christina Krawiec

Marshall Styczinski

Farnaz Mohseni

Ferdinand P. Beer, E. Russell Johnston, Jr., David F. Mazurek

Vector Mechanics for Engineers: Statics and Dynamics