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A turntable with mass m, radius R, and rotational
inertia (mR^2)/2 initially rotates freely about an axis
through its center at constant angular speed with
negligible friction. A piece of clay, also of mass m,
falls vertically onto the turntable, and sticks to it at point P, a distance R/2 from the
center of rotation.

What is the rotational inertia of the clay-turntable
system after the collision?
A) 1/4 mR^2
B) 1/2mR^2
C) 3/4 mR^2
D) mR^2
E) 2mR^2

Sagot :

The clay-turntable system's rotational inertia after strike will be (2/3)mR². Then the correct option is C.

What is rotational inertia?

The summation of the product of the mass of each particle with its square of the distance from the rotational axis is the moment of inertia, which is the amount denoted by the body resistant angular acceleration.

A turntable with mass m, radius R, and rotational inertia (mR²)/2 initially rotates freely about an axis through its center at constant angular speed with negligible friction.

A piece of clay, also of mass m, falls vertically onto the turntable and sticks to it at point P, a distance R/2 from the center of rotation.

Then the clay-turntable system's rotational inertia after strike will be

[tex]\rm I = I_0 + m *\dfrac{ R^2}{2}\\\\I = m* \dfrac{R^2}{2^2} + m * \dfrac{R^2}{2}\\\\I = \dfrac{3}{4}mR^2[/tex]

More about the rotational inertia link is given below.

https://brainly.com/question/22513079

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