## Newton’s Second Law for Rotation

10.7 Newton’s Second Law for Rotation

### Learning Objectives

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

- Calculate the torques on rotating systems about a fixed axis to find the angular acceleration
- Explain how changes in the moment of inertia of a rotating system affect angular acceleration with a fixed applied torque

**Practice!**

Practice 10.7.1 |
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A glider of mass m _{1} on a frictionless horizontal track is connected to an object of mass m_{2} by a massless string. The glider accelerates to the right, the object accelerates downward, and the string rotates the pulley. What is the relationship among T_{1} (the tension in the horizontal part of the string), T_{2} (the tension in the vertical part of the string), and the weight m_{2}g of the object? |

(a) m_{2}g = T_{2} = T_{1 } |

(b) m_{2}g > T_{2} = T_{1 } |

(c) m_{2}g > T_{2} > T_{1 } |

(d) m_{2}g = T_{2} > T_{1 } |

(e) none of the above |

**Discuss!**

Consider how you would answer these questions. Then bring this to class for a group discussion.

A bucket of water with a mass of 2.0 kg is attached to a rope that is wound around a cylinder. The cylinder has a mass of 3.0 kg and is mounted horizontally on frictionless bearings. The bucket is released from rest.

(a) Find the acceleration of the bucket.

(b) Find the tension in the rope.

(c) What is the speed of the bucket after it has fallen through a distance of 0.8 m?