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Can someone explain to me the solution of this problem please and why VB=(-20i) rad/s? Why rC/B=(4i-4k)in?

Can someone explain to me the solution of this problem please and why VB=(-20i) rad/s? Why rC/B=(4i-4k)in?

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Can someone explain to me the solution of this problem please and why VB=(-20i) rad/s? Why rC/B=(4i-4k)in?

 

76.2 2:47 PM "O. A 29 K/s USM-CEN 2-BSABE-B Calculate the velocity of coll ar B. VB = Oxr3 V3 = (4k)×(5j) V3 =(-20i)in./s LIT 111A: Literature I hilipp Calculate the accelerati on of collar B. a; = [4k×(-20i)]+[(3k)×(5j)] %3D a3 =(-15i – 80j)in./s? Calculate the velocity of collar C relative to the collar B. C/B VCB =(-3k)+(2i)x(4i – 4k) VCE = (8j- 3k)in./s Calculate the accelerati on of collar Crelative to the collar B. j-Sk +[(2i)×(-3k)]+[(8i)×(4i-4k)] +[(21)×(8j- 3k)] acB acs- j-8k +[(6i)]+[(32i)]+[(16k +6j]} aCB =(-2.25i +44j + 8k)in./s? Calculate the velocity of collar C. Vc =V3+0xrcB+ VC/B Vc =(-20i)+(4k)x(4i – 4k)+(8j– 3k) Vc =(-20i)+(16j)+(8j – 3k) Vc =(-20i +24j- 3k )in./s Calculate the accel eration of collar C. ac = a3 +(óxrc3)+ox(@xrc3)+(2oxv3)+acB [(-15i – 80j) +[(3k)×(4i – 4k)]+(4k)x(4kx(4i- 4k) ac (+(2(4k)x(8i – 3k))+(-2.25i + 44j+8k) | (-15i -80j) + [(12)]+(4k)×(16j)] ac (+(64j) +(-2.25i+ 44j+8k) ac = {(-15i – 80j)+[(12j)]+(-64i)+(64j)+(-2.25i + 44j + 8k %3D ac =(-145i- 24j+ 8k)in./s²
Transcribed Image Text:76.2 2:47 PM "O. A 29 K/s USM-CEN 2-BSABE-B Calculate the velocity of coll ar B. VB = Oxr3 V3 = (4k)×(5j) V3 =(-20i)in./s LIT 111A: Literature I hilipp Calculate the accelerati on of collar B. a; = [4k×(-20i)]+[(3k)×(5j)] %3D a3 =(-15i – 80j)in./s? Calculate the velocity of collar C relative to the collar B. C/B VCB =(-3k)+(2i)x(4i – 4k) VCE = (8j- 3k)in./s Calculate the accelerati on of collar Crelative to the collar B. j-Sk +[(2i)×(-3k)]+[(8i)×(4i-4k)] +[(21)×(8j- 3k)] acB acs- j-8k +[(6i)]+[(32i)]+[(16k +6j]} aCB =(-2.25i +44j + 8k)in./s? Calculate the velocity of collar C. Vc =V3+0xrcB+ VC/B Vc =(-20i)+(4k)x(4i – 4k)+(8j– 3k) Vc =(-20i)+(16j)+(8j – 3k) Vc =(-20i +24j- 3k )in./s Calculate the accel eration of collar C. ac = a3 +(óxrc3)+ox(@xrc3)+(2oxv3)+acB [(-15i – 80j) +[(3k)×(4i – 4k)]+(4k)x(4kx(4i- 4k) ac (+(2(4k)x(8i – 3k))+(-2.25i + 44j+8k) | (-15i -80j) + [(12)]+(4k)×(16j)] ac (+(64j) +(-2.25i+ 44j+8k) ac = {(-15i – 80j)+[(12j)]+(-64i)+(64j)+(-2.25i + 44j + 8k %3D ac =(-145i- 24j+ 8k)in./s²
*20-44. At the instant shown, the rod AB is rotating about the z axis with an angular velocity an = 4 rad/s and an angular acceleration o =3 rad/s2. At this same instant, the circular rod has an angular motion relative to the rod as shown. If the collar C is moving down around the circular rod with a speed of 3 in./s, which is increasing at 8 in./s, both measured relative to the rod, determine the collar's velocity and acceleration at this instant. Step 1 We are provided with the following data: The angular velocity of the rod AB is N = 4krad/s. The angular acceleration of the rod AB is N = 3krad/s². W1 = 4 rad/s w = 3 rad/s2 The length of the rod AB is rB = 5jin. A The angular velocity of collar C with respect to B is NC/B = 2irad/s. В 5 in. The angular acceleration of collar C with respect to B is w2 = 2 rad/s 8 rad/s2 İC/B = 8irad/s?. The distance between collar C with respect to point B is 4 in. rc/в 3 (4i — 4k) in. Prob. 20-44
Transcribed Image Text:*20-44. At the instant shown, the rod AB is rotating about the z axis with an angular velocity an = 4 rad/s and an angular acceleration o =3 rad/s2. At this same instant, the circular rod has an angular motion relative to the rod as shown. If the collar C is moving down around the circular rod with a speed of 3 in./s, which is increasing at 8 in./s, both measured relative to the rod, determine the collar's velocity and acceleration at this instant. Step 1 We are provided with the following data: The angular velocity of the rod AB is N = 4krad/s. The angular acceleration of the rod AB is N = 3krad/s². W1 = 4 rad/s w = 3 rad/s2 The length of the rod AB is rB = 5jin. A The angular velocity of collar C with respect to B is NC/B = 2irad/s. В 5 in. The angular acceleration of collar C with respect to B is w2 = 2 rad/s 8 rad/s2 İC/B = 8irad/s?. The distance between collar C with respect to point B is 4 in. rc/в 3 (4i — 4k) in. Prob. 20-44
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