Question

A uniform cylindrical turntable of radius 1.60 m and mass 27.7 kg rotates counterclockwise in a horizontal plane with an initial angular speed of 4π rad/s. The fixed turntable bearing is frictionless. A lump of clay of mass 2.47 kg and negligible size is dropped onto the turntable from a small distance above it and immediately sticks to the turntable at a point 1.50 m to the east of the axis. (a) Find the final angular speed of the clayand turntable.

Answer 1

`\omega_f = 3.46\pi`

Step-by-step explanation:

As we know that there is no external torque on the system of disc and the sand

so the angular momentum of the system will remains conserved

so here we can say

`L_i = L_f`

`I_o\omega = (I_o + mr^2)\omega_f`

here we know that

`I_o = (1)/(2)mR^2`

`I_o = (1)/(2)(27.7)(1.60)^2 = 35.46 kg m^2`

Now from above equation

`35.46(4\pi) = (35.46 + 2.47(1.5^2))\omega_f`

`35.46(4\pi) = 41.02\omega_f`

`\omega_f = 3.46\pi`