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Question

A disc rotates about a fixed axis. Its angular velocity ω varies with time according to the equation ω=at + b. Initially at t = 0 its angular velocity is 1.0 rad/s and angular position is 2 rad; at the instant t= 2s angular velocity is 5.0 rad/s. Determine angular position θ and angular acceleration when t = 4s.

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Solution

We have
w=at+b
at t=Os,w=1 rod/s
So, 1=O+b
At t=2 & w=5 rod/s
so, 5=2a+1
a=2 rod/s2
w=2t+1
α=dwdt=d(2t+1)dt=2 rad/s
w=dθdt=(2t+1)dt
dθ=(2f+1)dt
dθ=(2f+1)dt
[θ]θθ0=[t2+t]t0
θ2=t2+t
θ=t2+t+2

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