1.A sling is a traditional weapon that puts a heavy rock in a string or cloth ha

Question

1.A sling is a traditional weapon that puts a heavy rock in a string or cloth harness and swings it around in a single full circle before releasing it. An illustration is shown above. A. Imagine a sling that is 80 cm long and holds a 50 g rock. Assume the sling itself is massless. What is the moment of inertia of the rock in the sling? B. If the sling is accelerated constantly over that full circle and completes the circle in 0.5 s, what is the speed of the rock in m/s when it is released? C. How much torque is required to sling the rock?

Explanation / Answer

Here,
length oof sling, l = 80cm = 0.80 m
mass of rock, m = 50g = 0.050 kg
sling is massless,

Part A:
Moment of inertia, I

I = I for rock ( as sling is massless)
I = m*l^2
I = 0.050 * 0.80^2
I = 0.04 kg.m^2

Part B:
angular speed = 2*pi/t
w = 2*3.14/0.5
w = 12.56 rad/s

also
Linear speed = Angular speed * Radius
v = 12.56 * 0.80
v = 10.048 m/s

Part C:
Torque = Rate of change of Angular momentum / time
t = m*w*r^2/T

where:
? = angular velocity in radians per second.
m = mass of rock
r = length of sling
T = Time

t = 0.050 * 12.56 * 0.80^2 / 0.5
t = 0.804 N.m

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