- #1
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Homework Statement
A pulley with a rotational inertia of ##10^{-3}\frac {kg} {m^2}## about its axle and a radius of ##10 cm##, is acted on by a force applied tangentially at its rim.The force magnitude varies with time as
##F=0.5t+0.3t^2## , with ##F## in Newtons and ##t## in seconds.The pulley is initially at rest At ##t=3.0s## what are its (a) angular acceleration (b) angular speed ?
Homework Equations
##τ(t)=F(t)rsinθ##
##w-w_0=∝(t)Δt##
##τ(t)=I∝(t)##
The Attempt at a Solution
The confusing part for me is that F varies with time so from that angular acceleration will vary with time also torque will vary with time.
##τ(t)=F(t)rsinθ## ,
##sinθ## is always ##1## so ##τ(t)=F(t)r## is our equation.
And we also know that ##τ(t)=I∝(t)##
so
##F(t)r=I∝(t)## then ,
##∝(t)=\frac {F(t)r} {I}##
##∝(t)=420\frac {rad} {s^2}##
for B I wrote,
##w-w_0=∝(t)Δt## the object is initally at rest so ##w_0=0## then ##w=420\frac {rad} {s^2}.3s## which its
##w=1260\frac {rad} {s}##
but answer says its ##w=500\frac {rad} {s}##
where I am going wrong ?
Thanks