A metal disk with a radius of 10 cm and a mass of 6 kg has a hole in the center
ID: 1310598 • Letter: A
Question
A metal disk with a radius of 10 cm
and a mass of 6 kg has a hole in the center and is
nailed to a wooden post. The disk is free to rotate
without friction. Two small lightweight rockets are
glued to opposite sides of the disk, as shown. The
disk is initially at rest. Then the rockets are fired and
the disk is made to rotate by the rockets, which each
exert a force of 8N.
(a) What is the moment of inertia of the disk?
(b) What is the torque created by one of the rockets on the disk?
(c) What is the total torque created by both rockets on the disk?
(d) What is the angular acceleration of the disk?
(e) What is the total distance traveled by one of the rockets during the first two seconds
of rotation?
Explanation / Answer
a)moment of inertia of the disk=0.5MR^2 =0.5*6*.1*.1=0.03 Kgm^2 (ans)
b)torque created by one of the rockets on the disk=FR=8*0.1=0.8 Nm (ans)
c) total torque created by both rockets on the disk=8+8)*0.1=1.6 Nm (ans)
d)angular accleration=T/MOI=1.6/0.03=53.33rad/sec^2 (ans)
e) total distance traveled by one of the rockets during the first two seconds
of rotation=0.5 a*t^2=0.5*53.33*2*2=106.66 rad
and 2pi rad=2*3.14*0.1 m distance=0.628m
so 106.66 rad=10.66 m (ans)