Question

A particular horizontal turntable can be modeled as a uniform disk with a mass of 220 g and a radius of 25.0 cm that rotates without friction about a vertical axis passing through its center. The initial angular speed of the turntable is 5.00 rad/s. A ball of clay, with a mass of 50.0 g, is dropped from a height of 25.0 cm above the turntable. It hits the turntable at a distance of 15.0 cm from the middle, and sticks where it hits. Assuming the turntable is firmly supported by its axle so it remains horizontal at all times, find the final angular speed of the turntable-clay system. _______ rad/s

Answer 1

the final angular speed of the turntable-clay system.4.0914 rad/s

Step-by-step explanation:

mass M= 220g

radius R= 25.0 cm

angular velocity ω = 5.00 rad/s

Initial angular momentum
`L_i = I\omega = MR^2\omega/2`

or,
`L_i= 0.22*0.25^2*5/2`= 3.4×10^-2 kg-m^2/s

when the clay sticks to the turntable the moment of inertia is

`I_f =(MR^2)/(2)+mr^2= (0.22*0.25^2)/(2) +0.05*0.15^2`

= 8.31×10^(-3) kg-m^2

Let the final angular velocity be ω_f

then, since, initial angular momentum= final angular momentum

⇒ 3.4×10^-2= 8.31×10^(-3)×ω_f

ω_f = 4.0914 rad/sec

the final angular speed of the turntable-clay system.4.0914 rad/s