Question

A very thin 2.0-kg disk with a diameter of 80 cm is mounted
horizontally to rotate freely about a central vertical axis. On the
edge of the disk, sticking out a little, is a small, essentially
massless, tab or "catcher." A 2.0-g wad of clay is fired at a speed
of 14.0 m/s directly at the tab perpendicular to it and tangent to
the disk. The clay sticks to the tab, which is initially at rest,
at a distance of 40 cm from the axis.

(a) What is the moment-of-inertia of the clay about the axis?

kg·m^{2}

(b) What is the moment-of-inertia of the disk about the axis?

kg·m^{2}

(c) What is the moment-of-inertia of both clay and disk about the
axis?

kg·m^{2}

(d) What is the linear momentum of the clay before impact?

kg·m/s

(e) What is the angular momentum of the clay with respect to the
axis just before impact?

kg·m^{2}/s

(f) What is the angular speed of the disk after impact?

rad/s

Answer #1

moment of inertia of clay about the axis = mass * radius^2

moment of inertia of clay about the axis = 2 * 10^-3 * 0.4^2

**moment of inertia of clay about the axis = 0.00032
kg.m^2**

moment of inertia of disk = 0.5 * mass * radius^2

moment of inertia of disk = 0.5 * 2 * 0.4^2

**moment of inertia of disk = 0.16 kg.m^2**

total moment of inertia = 0.00032 + 0.16

**total moment of inertia = 0.16032 kg.m^2**

linear momentum of clay = mass * velocity

linear momentum of clay = 2 * 10^-3 * 14

**linear momentum of clay = 0.028 kg.m/s**

angular momentum of clay = mvr

angular momentum = 2 * 10^-3 * 14 * 0.4

**angular momentum of clay = 0.0112 kg.m/s**

by conservation of momentum

initial momentum = final momentum

0.0112 = 0.16032 * angular speed of disk

**angular speed of disk = 0.0698 rad/sec**

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