# Rotational kinetic energy and angular momentum

### Introduction

### Examples

#### Lessons

- A bowling ball with a mass on 5.0kg and radius of 12.0cm is rolling down an inclined surface with a negligible friction without slipping. If it starts from rest at a vertical distance of 1.5m, what will be the speed of the ball when it reaches the bottom of the inclined surface?
- A sphere of radius 24.0 cm and mass of 1.60 kg, starts from the rest and rolls without slipping down a 30.0° incline that is 12.0m long.
- Two masses $m_{1}$ = 16.0kg and $m_{2}$ = 24.6kg, are connected by a rope that hangs over a uniform pulley with a mass of 6.50kg and radius of 0.24m. Initially, $m_{1}$ is on the ground and $m_{2}$ rests 2.00m above the ground. If the system is released what will be the speed of $m_{2}$, as it hits the ground?
- A 2.6kg uniform cylindrical grinding wheel of radius 16cm makes 1600rpm.
- The speed of a skater increases from 2.0 rev every 4.0s to a final rate of 4.0 rev/s. If her moment of inertia was 4.4kg.m
^{2}, what is her final moment of inertia? - A potter's wheel is rotating around a vertical axis through its center at a frequency of 1.2 rev/s. The wheel can be modeled as a uniform disk of mass 4.0kg and diameter of 0.60m. The potter the throws a 2.1 kg chunk of clay, shaped as a flat disk of radius 6.0cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?