(a)
the moment of inertia of each system will be
for the system A
I = m1 r12
+ m2 r22 + m3 r32
= (8.40 kg) (0 m)2
+ (5.2 kg) (3.00 m)2 + (5.00 kg) (5.00 m)2
= ......... kg.m2
for the system B
I = m1 r12
+ m2 r22 + m3 r32
= (8.4 kg) (5.00 m)2
+ (5.2 kg) (4.00 m)2 + (5.0 kg) (0 m)2
= ......... kg.m2
(b)
if same force of magnitude F = 446 N the torque
will not be the saeme
we know that
τ = F l
where l = 3.00 m
in the system B the lever arm is l
= 0, since the line of action of the force passes through the axis
of rotation
for the system A the torque will be
τ = - F l
= - (446 N) (3.00 m)
= ....... N.m
for the system B the torque will be
τ = F l
= (446 N) (0 m)
= 0 N.m
(c)
the equation for the angular velocity
is givenn by
ω = ωo + α t
but α = (Σ τ / I)
where Σ τ is the net torque and I is the moment
of inertia
in both the systems start from rest the initial
angular velocity ωo = 0 rad/s
final angular velocity are after t = 10 s
for system A
ω = ωo + (Σ τ / I)
t
= ........ rad/s
for system B
ω = ωo + (Σ τ / I)
t
= ........ rad/s