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(II) For the vectors shown in Fig. $38,$ determine $(a) \vec{\mathbf{B}}-2 \vec{\mathbf{A}}$ ,(b) $2 \vec{\mathbf{A}}-3 \vec{\mathbf{B}}+2 \vec{\mathbf{C}}$

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a. $-92.4 \hat{\mathrm{i}}-19.4 \hat{\mathrm{j}}$b.$122.0 \hat{\mathrm{i}}-86.6 \hat{\mathrm{j}}$

Physics 101 Mechanics

Chapter 3

Kinematics in Two or Three Dimensions; Vectors

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

Rotation of Rigid Bodies

Dynamics of Rotational Motion

Equilibrium and Elasticity

University of Washington

University of Sheffield

University of Winnipeg

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02:34

In physics, a rigid body is an object that is not deformed by the stress of external forces. The term "rigid body" is used in the context of classical mechanics, where it refers to a body that has no degrees of freedom and is completely described by its position and the forces applied to it. A rigid body is a special case of a solid body, and is one type of spatial body. The term "rigid body" is also used in the context of continuum mechanics, where it refers to a solid body that is deformed by external forces, but does not change in volume. In continuum mechanics, a rigid body is a continuous body that has no internal degrees of freedom. The term "rigid body" is also used in the context of quantum mechanics, where it refers to a body that cannot be squeezed into a smaller volume without changing its shape.

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In physics, rotational dynamics is the study of the kinematics and kinetics of rotational motion, the motion of rigid bodies, and the about axes of the body. It can be divided into the study of torque and the study of angular velocity.

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For the vectors shown in F…

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(II) For the vectors shown…

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(II) For the vectors give…

17:53

(II) For the vectors given…

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For the vectors given in F…

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00:35

Given vectors $\mathbf{u}$…

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(II) Determine the vector …

01:42

$31-36$ Find $2 \mathbf{u}…

02:14

Find $2 \mathbf{u},-3 \mat…

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Sketch $2 \mathbf{v},-\mat…

01:52

Sketch the vector sum $\ma…

so here before we do anything we need to find the X and my components of A B and C So ace of X beast of X, cease of X, Let's solve. Ah, this is gonna be 44.0 coastline of 28 degrees. This is gonna be negative. 26.5 co sign of 56 degrees. This will be 31.0 times co sign of 270 degrees. Let's solve. So this is gonna be 38.85 This will be, ah, negative 14.82 and this will be zero um, a sub y is gonna be 44.0 sign of 28 degrees be sub y with equal 26.5 signs of 56 degrees and C sub or I would equal 31 0.0 co star sign of 270 degrees. We can automatically say that this is gonna be negative 31.0. This is gonna be 21.97 and this is equaling 20.66 And so now we can solve for a Let's This is gonna new fourth book for Per day. Ah, we have B minus two times a. Let's evaluate the X component first, so this will be negative. 14.82 minus two times positive. 38.85 This is giving us negative. 92.52 Let's do the Y component. Ah, this will be 21.97 minus two times 20.66 This is giving us a negative 19.35 And so, um, both components are negatives. So here it'll be the third quadrant. And, uh, given this weekend, uh, let's do the vector form J hat and then find the, uh, Magnitude. So this will be the square root of the sum of the squares. Negative. 92.52 quantity squared plus negative 19.35 quantity squared all to the 1/2 power. This is giving us 94.5 approximately, and then we can solve for theta the angle. This will be arc tanne of the why component, uh, 19.35 divided by the x component 92.52 And this is equaling 11.8 degrees. And this would be a blow negative. X axis in order for the vector toe lie again in the third quadrant. So this would be our magnitude, and this would be our direction for B. We have that two times a minus three B plus two C. Let's do the X component first. This will be two times 38.8 five minus three times negative. 14.82 huh? My apologies for being cramped. Plus two times, uh, 0.0. And this is equaling. 122.16 Let's do the Y component. This is equaling two times 20.66 a minus, three times 21.97 and then plus two times negative. 31.0. This is giving us negative 86.59 and we have a positive X and a negative. Why? So this is gonna lie in the fourth quadrant again. We want to find the magnitude, and this is gonna equal 122.16 squared plus negative 86.59 squared all to the 1/2 power. And this is equaling, uh, 100 50 approximately. Um, my apologies. Let's write it in vector form as well. Ah, 122.16 You always wonder I didn't factor for him. Ah, simply giving the components is not enough. Because we wanna We want to write the eye hat and the J hat. So negative 86.59 j So that would be the vector form. And then finally we can go to the angle. This will be our tan of the wide component divided by the X component. So this will be 86.59 What about 122.16 And this is giving us approximately 35.3 degrees. And you always have Thio take into account which quadrant is lying. It is lying in the fourth quadrant, so this will be 35.3 degrees below positive x access. So this would be our magnitude and this would be our direction. That is the end of the solution. Thank you for watching

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