Mechanics> 5...

A solid body rotates about a stationary axis according to the law theta=at-bt^3,where a=6 rad/s and b=2 rad/s^3.Find the mean values of the angular velocity and acceleration over the interval between t=0 and the time,when the body comes to rest.

rajan jha , 15 Years ago

Grade 12

1 Answers

vikas askiitian expert

@ = at - bt³ ...............1

d@/dt = W = a-3bt² ...............2

dW/dt = alfa = -6bt ............3

body comes to rest when angular velocity becomes 0

a - 3bt² = 0

t = (a/3b)^1/2

mean value of angular velocity = (@_t - @₀)/t

@₀=0

@_t= a(a/3b)^1/2 - b(a/3b)^3/2

= a(a/3b)^1/2[1-1/3]

=(2a/3)(a/3b)^1/2

mean value of angular velocity = 2a/3(a/3b)^1/2/t = 2a/3 = 4rad/sec

now mean value of angular accleration = change in angular velocity/t = (W_t-W₀)/t

at t=0 W=a , at T=t W_t = 0

mean value = a/t = (3ab)^1/2

=(36)^1/2=6rad/sec²

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Last Activity: 15 Years ago

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Mechanics> 5...

A solid body rotates about a stationary axis according to the law theta=at-bt^3,where a=6 rad/s and b=2 rad/s^3.Find the mean values of the angular velocity and acceleration over the interval between t=0 and the time,when the body comes to rest.

rajan jha , 15 Years ago

vikas askiitian expert

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