The disk rolls without slipping on the horizontal surface. If the disk has a clockwise angular velocity of wo 18 rad/s and a counterclockwise angularacceleration of 6.5 rad/s2 determine the velocity and acceleration of pin A relative to the slotted member BC and the angular velocity and angularacceleration of BC. The value of r is 235 mm. Neglect the distance from the center of pin A to the edge of the disk. The relative velocity and accelerationare positive if they point from B to Cand negative if they point from C to B. The angular velocity and acceleration are positive if counterclockwise andnegative if clockwise.59Om3.0 rAnswers:m/siVrelm/s2arelrad/sШвсrad/s2авсIl

Question
Asked Jul 8, 2019
The disk rolls without slipping on the horizontal surface. If the disk has a clockwise angular velocity of wo 18 rad/s and a counterclockwise angular
acceleration of 6.5 rad/s2 determine the velocity and acceleration of pin A relative to the slotted member BC and the angular velocity and angular
acceleration of BC. The value of r is 235 mm. Neglect the distance from the center of pin A to the edge of the disk. The relative velocity and acceleration
are positive if they point from B to Cand negative if they point from C to B. The angular velocity and acceleration are positive if counterclockwise and
negative if clockwise.
59
Om
3.0 r
Answers:
m/s
i
Vrel
m/s2
arel
rad/s
Швс
rad/s2
авс
Il
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The disk rolls without slipping on the horizontal surface. If the disk has a clockwise angular velocity of wo 18 rad/s and a counterclockwise angular acceleration of 6.5 rad/s2 determine the velocity and acceleration of pin A relative to the slotted member BC and the angular velocity and angular acceleration of BC. The value of r is 235 mm. Neglect the distance from the center of pin A to the edge of the disk. The relative velocity and acceleration are positive if they point from B to Cand negative if they point from C to B. The angular velocity and acceleration are positive if counterclockwise and negative if clockwise. 59 Om 3.0 r Answers: m/s i Vrel m/s2 arel rad/s Швс rad/s2 авс Il

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Expert Answer

Step 1

Draw the triangle formed by joining the points OAB.

 

C
A
590
B
3r
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C A 590 B 3r

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Step 2

Apply sine rule.

 

OA
ОВ
sin 180° - (B+59)
sin B
3r
sin B sinB 59°)
1
3
sin B
sin Bcos59° + cos Bsin 59°
1
sin B 0.515 sinB+0.857 cos B
0.515 0.857 cotB = 3
B 19.03°
Obtain the distance between A and B
АВ
OA
sin B
sin 59°
0.235 m
АВ
sin 59°
sin 19.03°
AB 0.6178 m
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OA ОВ sin 180° - (B+59) sin B 3r sin B sinB 59°) 1 3 sin B sin Bcos59° + cos Bsin 59° 1 sin B 0.515 sinB+0.857 cos B 0.515 0.857 cotB = 3 B 19.03° Obtain the distance between A and B АВ OA sin B sin 59° 0.235 m АВ sin 59° sin 19.03° AB 0.6178 m

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Step 3

Obtain the position vector of O with respe...

FoD= OD[cos(90°-)i-sin (90°- p)]]
roD 0.235 m[cos(90°-19.03°)i- sin (90° -19.03°)j]
roD 0.0766i 0.2222j
Obtain the velocity at O
Vo- VD + 0 xгоD
Vo 0+18k x (0.0766i - 0.2222j
Vo 1.3788j+3.9996i m/s
Obtain the position vector of.4 with respect to O
4o AO-cos(59+ P)i-sin(59° + B)j]
r4o 0.235-cos(59° +19.03°)i-sin (59° +19.03°)j]
o0.0487i -0.2299j
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FoD= OD[cos(90°-)i-sin (90°- p)]] roD 0.235 m[cos(90°-19.03°)i- sin (90° -19.03°)j] roD 0.0766i 0.2222j Obtain the velocity at O Vo- VD + 0 xгоD Vo 0+18k x (0.0766i - 0.2222j Vo 1.3788j+3.9996i m/s Obtain the position vector of.4 with respect to O 4o AO-cos(59+ P)i-sin(59° + B)j] r4o 0.235-cos(59° +19.03°)i-sin (59° +19.03°)j] o0.0487i -0.2299j

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