Question

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

Answer 1

Answer:

Explanation:

That what I can do...

ω=at+b......(1)

Again we know

ω=ω০+αt.......(2)

Comparing both (1) and (2)

b=ω০ and a=α

Now,

at t=0 ω=1,

then ω০=1 rad/s

Now,

ω=ω০+αt

or, dθ/dt= ω০/αt

or, dθ= ω০dt +αt dt

Integrating both sides...

θ= ω০t+1/2αt^2........(3)

Again,

at t=2 ω=5

then α=2 rad/s^2 [ putting values in eqn (2)]

Finally putting the values in eqn (3) at t=4

we get θ= 20 rad