16–147. If the slider block C is fixed to the disk that has aconstant counterclockwise angular velocity of 4 rad/s,determine the angular velocity and angular acceleration ofthe slotted arm AB at the instant shown.40 mm60 mm30w = 4 rad/s180 mm60°

Answered: 16–147. If the slider block C is fixed…

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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Question

16–147. If the slider block C is fixed to the disk that has a
constant counterclockwise angular velocity of 4 rad/s,
determine the angular velocity and angular acceleration of
the slotted arm AB at the instant shown.
40 mm
60 mm
30
w = 4 rad/s
180 mm
60°

Expert Solution

Step 1

Given

Angular rotation = 4 rad/s

To find

Angular velocity

Angular acceleration

Step 2

$A s p e r t h e r e l a t i o n o f l i n e a r v e l o c i t y t o a n g u l a r v e l o c i t y \Rightarrow V = ω r \Rightarrow V = 4 \times \frac{60}{1000} = 0.24 m / s V e c t o r i c a l l y i t c a n b e w r i t t e n \Rightarrow \vec{V_{C}} = - V_{C} \sin 30 \vec{i} - V_{C} \sin 30 \vec{j} \Rightarrow \vec{V_{C}} = - 0.24 \sin 30 \vec{i} - 0.24 \sin 30 \vec{j} = (- 0.12 i - 0.2078 j) m / s_________a S l i d e r v e l o c i t y a c c o r d i n g t o t h e b l o c k C \Rightarrow \vec{V_{C}} = \vec{V_{A}} + {\vec{ω}}_{A B} \times {\vec{r}}_{C A} + {\vec{V}}_{C A} \Rightarrow \vec{V_{C}} = 0 + {\vec{ω}}_{A B} k \times \frac{180}{1000} j + - {\vec{V}}_{C A} j \Rightarrow \vec{V_{C}} = (- 0.18 {\vec{ω}}_{A B} i + - {\vec{V}}_{C A} j) m / s_______b C o m p a r i n g e q u a t o n a a n d b F o r x c o m p o n e n t \Rightarrow {\vec{ω}}_{A B} = \frac{0.12}{0.18} = 0.666 r a d / s F o r y c o m p o n e n t \Rightarrow {\vec{V}}_{C A} = 0.2078 m / s$

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