Class Notes 30 November Turn in HW Today:

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Class Notes 30 November Turn in HW Today: Use rotational fundamental four Did you write your basic, unadulterated, starting equations? Today: Moment of Inertia Rotational analog to F=ma

Example A bolt is tightened to a torque of 136 N·m (100 ft-lb). A person capable of exerting 300. N has a 30.0-cm-long wrench. Can he loosen it? Other methods: Get stronger, lubricate bolt, heat/cold bolt (possibly) NO! He needs a 45.3 cm wrench.

Lever Arm Component Serway, College Physics 6/e

Serway, College Physics 6/e

Spark Plugs

Rotational Dynamics tP= I a What happens when a net torque is applied to a rigid object? Consider a point object, of mass m, constrained at r. An unbalanced torque on an object causes an angular acceleration! Find Torque = (mr2). Generalize to P = (miri2). Define the “moment of inertia” = I = (miri2) tP= I a

Moment of Inertia I  Smiri2 Treat ANY rigid object as a collection of point masses! The moment of inertia of an object is a measure of its resistance to changes in rotational motion. In general: mass The “mass / linear” comes in after equation. Relate rotational ideas back to linear motion. linear I  Smiri2

Moment of Inertia Analogy A physical analogy: A beautiful painting in St Peters (Vatican) … until you get closer and realize that it’s really a bunch of small tiles. Now show 2 C-clamps attached to two meter sticks, one at ends and one near middle. Race teacher vs. student. This leads to the definition on next slide

Moment of Inertia Rotational analogue to mass Different for various objects Only depends on physical characteristics (size & shape) The mass, where the mass is located, & the axis of rotation Some common examples are disk, sphere, hoop, cylinder... After “Different…”, ask students about the moment of inertia…Can they figure out the next two bullets?

Consider three objects, a solid sphere, a hollow sphere, and a disk, each of equal mass and equal outside radius. Which has the highest moment of inertia? Solid sphere Hollow sphere Disk All the same More information is needed. 2016: Votes 6, 1, 1, 4, 0

Example A uniform disk is pushed tangentially with a 10.0 N force. It has a mass of 4.00 kg and a radius of 10.0 cm. Additionally a 0.200 N·m frictional torque opposes the motion. At what rate is it spinning after 5.00 s? w = 200. rad/s = 1910 rpm

Homework You should have read Chapter 8, sections 1-6 Do problems on Worksheet 34 Finish up (start?) the test rework. Due Friday at 5:00