## Rolling Motion

11.1 Rolling Motion

### Learning Objectives

By the end of this section, you will be able to:

- Describe the physics of rolling motion without slipping
- Explain how linear variables are related to angular variables for the case of rolling motion without slipping
- Find the linear and angular accelerations in rolling motion with and without slipping
- Calculate the static friction force associated with rolling motion without slipping
- Use energy conservation to analyze rolling motion

### Rolling Motion without Slipping

In this module, we will continue our discussion about rotational motion and extend it to rotating about a moving axis. The first example of this type of motion is rolling. In the animation below, you can see that rolling is a combination of two types of motion: rotation + translation. We can use this idea to determine the kinetic energy of rolling, because it is literally K_{rolling} = K_{rotation} + K_{translation}.

Practice 11.1.1 |
---|

A basketball rolls across a classroom floor without slipping, with its center of mass moving at a certain speed. A block of ice of the same mass is set sliding across the floor with the same speed along a parallel line. Which object has more kinetic energy? |

(a) The basketball does. |

(b) The ice does. |

(c) The two quantities are equal. |

**Practice!**

Practice 11.1.2 |
---|

A basketball rolls across a classroom floor without slipping, with its center of mass moving at a certain speed. A block of ice of the same mass is set sliding across the floor with the same speed along a parallel line. The two objects encounter a ramp sloping upward. Which object will travel farther up the ramp? |

(a) The basketball does. |

(b) The ice does. |

(c) The two quantities are equal. |

**Discuss!**

The solid, uniform disk rolls without slipping. What is its total kinetic energy?

A 3.50 kg section of thin-walled pipe with radius 0.110 m is rolling without slipping on a flat horizontal surface. A wind begins to blow with a force of 9.00 N directly against the pipe’s direction of movement. If the pipe is rotating at 12.0 radians per second when the wind begins to blow, how far will it roll into the wind before stopping?

A hoop, a disk, and a sphere, each of mass M and radius R, are released from rest at the top of a ramp of height h. Which will make it to the bottom of the ramp first, and why?

**Practice!**

Practice 11.1.3 |
---|

A solid bowling ball rolls down a ramp. Which of the following forces exerts a torque on the bowling ball about its center? |

(a) the weight of the ball |

(b) the normal force exerted by the ramp |

(c) the friction force exerted by the ramp |

(d) more than one of the above |

(e) depends on whether the ball rolls without slipping |