Rotational Kinetic Energy © 2014 Pearson Education, Inc.

Rotational Kinetic Energy We are familiar with the kinetic energy of a single particle moving along a straight line or in a circle. This allows us to use the work-energy approach to solve problems involving rotation.

Rotational Kinetic Energy The units for rotational kinetic energy can be kg•m2/s2 or N•m or J © 2014 Pearson Education, Inc.

Consider a disk rolling down a ramp without slipping Assuming the disk is initially at rest: What makes the disk start rolling? What is the translational speed of its center of mass when it reaches the bottom of the ramp? What is its angular velocity when it reaches the bottom of the ramp?

What makes the disk start rolling? The force of friction provides the torque! If the object is rolling without slipping, the friction force is static friction. If the ramp is frictionless, the disk will slide down without rotation.

What is the translational speed of its center of mass when it reaches the bottom of the ramp? The velocity and angular velocity at the bottom of the ramp can be calculated using energy conservation. 𝑈 𝑔 = 𝐾 𝑙𝑖𝑛𝑒𝑎𝑟𝑐𝑚 + 𝐾 𝑟𝑜𝑡𝑎𝑡𝑖𝑜𝑛𝑎𝑙𝑐𝑚 𝑚𝑔𝑦= 1 2 𝑚 𝑣 𝑐𝑚 2 + 1 2 𝐼 𝑐𝑚 𝜔 2 𝑣 𝑐𝑚 = 4𝑔ℎ 3 and 𝜔= 4𝑔ℎ 3 𝑅 2

What are the variables that the linear and rotational speed depend on?? The translational speed at the bottom only depends on gravity and the height of the ramp. The angular speed depends on the gravity and the height as well but it also depends on the radius of the object. Neither one depended on the mass of the object!!

How does the linear speed of an object on a frictionless ramp compare? Without friction the object would not roll down the ramp, it would only slide 𝑚𝑔𝑦= 1 2 𝑚 𝑣 2 𝑣= 2𝑔ℎ The linear speed of an object sliding down a frictionless ramp is faster than an object rolling down a ramp with friction!! 𝑣 𝑐𝑚 = 4𝑔ℎ 3

Rotational kinetic energy © 2014 Pearson Education, Inc.

Rotational kinetic energy © 2014 Pearson Education, Inc.

Flywheels for storing and providing energy In a car with a flywheel, instead of rubbing a brake pad against the wheel and slowing it down, the braking system converts the car's translational kinetic energy into the rotational kinetic energy of the flywheel. As the car's translational speed decreases, the flywheel's rotational speed increases. This rotational kinetic energy could then be used later to help the car start moving again.

Example 8.9 A 1600-kg car traveling at a speed of 20 m/s approaches a stop sign. If it could transfer all of its translational kinetic energy to a 0.20-m-radius, 20-kg flywheel while stopping, what rotational speed would the flywheel acquire?

Example 8.9 𝐾 𝑇𝑟𝑎𝑛𝑠𝑙𝑎𝑡𝑖𝑜𝑛𝑎𝑙 = 𝐾 𝑅𝑜𝑡𝑎𝑡𝑖𝑜𝑛𝑎𝑙 1 2 𝑚 𝑣 𝑖 2 = 1 2 𝐼 𝜔 𝑓 2 Answer: ωf=1264.9 rad/s

Take out a sheet of Notebook paper Lets write some stuff! Take out a sheet of Notebook paper 1. Write your FULL name in the top RIGHT corner 2. UNDER your name write the date (February 19th). 3. Title this “Energy in Physics”

AP Physic!! February 19th!! Write a minimum of one page WITHOUT YOUR NOTES: Using class concepts from the energy unit and at least three other units, explain how energy concepts are related or interrelated to multiple other units we have learned about. List of Units: Motion in 1D Projectiles Forces Gravitational and Circular Motion Momentum Rotational

#4 Rotational Kinetic Energy Assignment Page 314: 48-50,52 (a and b only!!), 55 (only answer the first question) and 56

© 2014 Pearson Education, Inc.

© 2014 Pearson Education, Inc.

© 2014 Pearson Education, Inc.