Answer:
The loss of initial Kinetic energy = 37.88 %
Explanation:
Given:
Rotational inertia of the turntable =
Rotational inertia () of the record =
According to the question:
<em>Frictional forces act to bring the record and turntable to a common angular speed.</em>
So,angular momentum will be conserved as it is an inelastic collision.
Considering the initial and final angular velocity of the turn table as respectively.
Note :
Angular momentum = Product of moment of inertia
and angular velocity
.
Lets say,
⇒ initial angular momentum = final angular momentum
⇒
⇒
⇒ ...equation (i)
Now we will find the ratio of the Kinetic energies.
⇒ ⇒
Their ratios:
⇒
⇒
Plugging the values of as
from equation (i) in the ratios of the Kinetic energies.
⇒
Now,
The Kinetic energy lost in fraction can be written as:
⇒
Now re-arranging the terms.
Plugging the values of and
.
⇒
To find the percentage we have to multiply it with and here negative means for loss of Kinetic energy.
⇒
So the percentage of the initial Kinetic energy lost is 37.88