Physics 218: Lecture 14 Chapter 8: Rotational Motion Torque and Newton’s Law Moment of inertia Physics 218 Fall 2010 Slide 1 Physics 218 Fall 2010 Supposing two people of equal strength grab onto either side of this tire and pull. What would the free body diagram look like? What could you say about the motion of the object? Physics 218 Fall 2010 Supposing two people of equal strength grab onto either side of this tire and pull. What would the free body diagram look like? What could you say about the motion of the object? 0 F No acceleration => a 0 constant velocity m Physics 218 Fall 2010 Supposing two people of equal strength grab onto either side of this tire and pull this way. What would the free body diagram look like? What could you say about the motion of the object? Physics 218 Fall 2010 Actually the same free body diagram applies … 0 No acceleration => F constant velocity a 0 m … for the center of mass Physics 218 Fall 2010 The thing that is different is that there is now a torque that produces rotation about a pivot point. Torque and rotational motion are the topics this week. Physics 218 Fall 2010 Physics 218 Fall 2010 We’ll need to describe the rotation of objects The whole object rotates as one, so it is sufficient to know the axis of rotation and the angle, Physics 218 Fall 2010 This is equivalent to the way we have described linear motion up to now x x And, if you understand linear motion, there is a rich set of analogies to exploit Physics 218 Fall 2010 Linear motion Rotational motion x position x angle x velocity v angular t velocity t v acceleration a angular t acceleration t F m a I Physics 218 Fall 2010 Quiz An object experiences zero net torque. Which of the following statements is true? Hint: zero net torque is analogous to zero net force. A.The object is not rotating. B.The object is rotating. C.The object has zero angular velocity. D.The object has constant angular velocity. E. All statements are false, including this one. Physics 218 Fall 2010 Relationship between rotation and linear motion In rotational motion, all points travel on a circle around the axis of rotation. Physics 218 Fall 2010 Relationship between rotation and linear motion s s r distance traveled s around arc radial distance to r center of rotation angle in radians Physics 218 Fall 2010 Demo 1Q-1: Rotational Motion Same angular distance. s r Physics 218 Fall 2010 15 Convert 60 degrees from degrees to radians : (rad) (degrees) 180 60 1 . 0472 radian 180 3 Physics 218 Fall 2010 Rotational motion Linear motion s angle distance s r along arc angular velocity v r velocity t v angular acceleration a r acceleration t Basically, to get the linear quantity, take the angular quantity (in radians) and multiply by r. Physics 218 Fall 2010 Quiz A wind turbine spins at 22 rpm (rotations per minute). The blades are 20 m long. What is the linear speed at the tip of the blade? A. 1.1 m/s B. 7.3 m/s C. 77 m/s D. 46.1 m/s Physics 218 Fall 2010 Quiz - CD Players Linear speed of the disk where the laser shines must be maintained at a constant value of 1.25 m/s. Does the disc spin faster when it is reading the inner or outer tracks on the disc? A. Inner B. Outer Physics 218 Fall 2010 19 Quiz Is the linear velocity at the very top of the rear wheel: A. greater than B. equal 4R C. less than R Front Rear the linear velocity at the top Wheel Wheel of the front wheel? Image from www.jackiechankids.com/ files/ATW.htm Physics 218 Fall 2010 20 Torque Torque, , is the rotational analog to Force. F ma I Torque, , involves a force, F F r The ability of a force to rotate an object depends on not only the magnitude of the force, but also depends on -where the force is applied -the direction in which the force is applied. Physics 218 Fall 2010 21 Torque The ability of a force to rotate an object depends on not only the magnitude of the force, but also depends on -where the force is applied -the direction in which the force is applied. Physics 218 Fall 2010 22 Torque F r FF sin Forces along the radial The component direction produce no torque.. to r produces prependicular torque. Physics 218 Fall 2010 23 Newton’s Second Law F ma I The moment of inertia, I, appears as a rotational mass. Physics 218 Fall 2010 24.