Question

A potter's wheel having a moment of inertia of 46 kg⋅m2 is spinning freely at 44 rpm . The potter drops a lump of clay onto the wheel, which sticks to the wheel at a distance 1.5 m from the rotational axis. Consequently, the wheel is spinning at 35 rpm . What is the mass of the lump of clay?

Answer 1

Answer:m=5.25 kg

Explanation:

Given

Initial angular momentum $I_1=46 kg-m^2$

$N_1=44 rpm$

$\omega _1=\frac{2\pi N_1}{60}=4.60 rad/s$

Potter drop a lump of clay such that speed decreases to 35 rpm

$N_2=35 rpm$

$\omega _2=\frac{2\pi \cdot 35}{60}=3.66 rad/s$

Moment of inertia after dropping lump of let say mass m

$I_2=46+m\times 1.5^2$

$I_1\omega _1=I_2\omega _2$

$46\times 4.6=I_2\times 3.66$

$I_2=57.81 kg-m^2$

$46+m\times 1.5^2=57.81$

$m=5.25 kg$