Question

# A billiard ball with a mass of m and a radius of r is rolling down...

```A billiard ball with a mass of m and a radius of r is rolling down without friction along an inclined plane with a slope of Θ at h height from the floor.

(1) Find an inertial moment for the center of a billiard ball. Here the mass distribution of billiard balls is assumed to be uniform.

(2) What is the speed of a billiard ball when it reaches the floor?
```

((1)If you can't solve the question yourself, use inertia moment I=2/5*mr^2.)

Solution :

Part (a) Solution :

Inertial moment for the center of a billiard ball : I = (2/5) m r2

.

Part (b) Solution :

Let the speed of the billiard ball when it reaches the floor is : v.

Then, Total kinetic energy of the billiard ball at the bottom of the inclined plane will be : KEtotal = KErot + KEtran

∴ KEtotal = (1/2) I ω2 + (1/2) m v2

∴ KEtotal = (1/2) {(2/5) m r2} (v/r)2 + (1/2) m v2

∴ KEtotal = (1/5) mv2 + (1/2) m v2

∴ KEtotal = (7/10) m v2

.

Now, According to the conservation of energy : KEf = PEi

∴ (7/10) m v2 = m g h

∴ (7/10) v2 = g h

∴ v2 = (10/7) g h

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