a kid on a playground swing makes 6 complete to-and-from swings each 30 seconds (a) the frequency of the swinging is? (b) the pe
2 answers:
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Answer:
a) total moment of inertia is 1359.05 kg m^2
b) angular acceleratio is 0.854rad/sec^2
Explanation:
Given data:
m1=6.9 kg
L=4.88 m
m2=34.5 kg
R=1.22 m
we klnow that moment of inertia for rod is given as
J1=(1/12) ×m×L^2
moment of inertia for sphere is given as
J1=(2/5) ×m×r^2
As object rotates around free end of rod then for sphere the axis around what it rotates is at a distance of d2=L+R
For rod distance is d1=0.5*L
By Steiner theorem
for the rod we get
for the sphere we get
And the total moment of inertia for the first case is
b) F=476 N
The torque for system is given as
where a is angle between Force and distance d
and where d represent distance from rotating axis.
In this case a = 90 degree
M=476*2.44 = 1161.44 Nm
The acceleration is calculated as
= 0.854 rad/sec^2