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smooth pins link the mechanism. when in the shown position, the angular velocity

ID: 1862401 • Letter: S

Question

smooth pins link the mechanism. when in the shown position, the angular velocity and angular acceleration of AB is 10 rad/s and 20 rad/s^2 clockwise. Find the angular velocities of BC and CD. Also find the angular acceleration of CD. I do not think what i did was right because i think i messed up the horizontal and vertical componants equation and math. Please give me a silution and I will rate.




smooth pins link the mechanism. when in the shown position, the angular velocity and angular acceleration of AB is 10 rad/s and 20 rad/s^2 clockwise. Find the angular velocities of BC and CD. Also find the angular acceleration of CD. I do not think what i did was right because i think i messed up the horizontal and vertical componants equation and math. Please give me a silution and I will rate.

Explanation / Answer

assume a x-axis along BA and y-axis along AC,

I will use vectors to solve this....

first, I will conduct the velocity anaysis,

vB= 2*10j=20j (i,j,k are the unit components of axes)

vC= vi (v is the unknown velocity and it is directed along i)

rCB= 2i + 3j

wCB= wk (w is the unknown angular velocity of CB)

Now,

vC=vB+ wCB*rCB (* is the cross-product)

Substitute,

vi= 20j+ wk*(2i+3j)

vi= 20j+ w(2j-3i)

vi= -3wi+(2w+20)j

Equating parts of i and j on both sides,

2w+20=0

w=-10 rad/s

v=-3w= 30 ft/s

Hence, you get the angular velocity....

Similarly,

aB= 10^2 * 2i+ 20*2j= 200i+ 40j

aC= ai

fCB= fk (f is the angular accelaration)

Substitute all these in the acceleration equation and separate the i and j parts to obtain the solution exactly as done above....In case of any doubts do comment, I will reply asap..