The right-angle bar rotates clockwise with an angular velocity which is decreasing at the rate of 4rad/s 2 . Write the vector expressions for the velocity and acceleration of point A when ω = 2 rad/s.
Text Solution
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Sol. Using the right-hand rule gives
ω = –2 k rad/s and α = +4 k rad/s 2 The velocity and acceleration of A become
[v = ω × r] v = –2k × (0.4i + 0.3j)
= 0.6i – 8j m/s Ans.
[a n = ω × ( ω × r)] a n = –2k × (0.6i – 0.8j)
= –1.6i – 1.2j m/s
2 [a t = α × r] a t = 4k × (0.4i + 0.3j)
= –1.2i + 1.6j m/s
2 [a = a n + a t ] a = –2.8i + 0.4j m/s
2 Ans.
The magnitudes of v and a are
v = 
= 1 m/s and
a = 
= 2.83 m/s 2
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