1. 5.2 Uniform Circular motion 5.3 Dynamic of Uniform Circular Motion Circular Motion HW4: Chapt.5: Pb.23, Pb.24, Pb.30, Pb.33, Pb.36, Pb.53- Due FRIDAY, OCT. 2

2. Applications of Newton’s Laws Involving Friction Example 5-3: Pulling against friction. A 10.0-kg box is pulled along a horizontal surface by a force of 40.0 N applied at a 30.0° angle above horizontal. The coefficient of kinetic friction is 0.30. Calculate the acceleration.

3. Uniform Circular Motion—Kinematics Uniform circular motion: motion in a circle of constant radius at constant speed Instantaneous velocity is always tangent to the circle.

4. Linear vs. Circular motion: Linear motionRelationshipAngular motion PositionAngle  DisplacementAngular displacement Average velocityAverage angular velocity Instantaneous velocity Instantaneous angular velocity

5. Uniform circular motion How far? –Angular displacement –The size of the angle swept out by the motion –Typically “+” indicates counter- clockwise –Units - radians Go around once: y x ii ff r  Uniform circular motion means Constant rotation speed 2 π radians 360 degrees 1 revolution

6. Uniform circular motion How fast? –Angular velocity –This is constant for Uniform circular motion –Units: rad/sec y x ii ff r  rpm-revolutions per minute rad/s

7. Relationship between angular and linear motion How far does it go? –Angular displacement,  to linear motion, s. –Here r is the radius of the circle in meters, and s is the distance traveled in meters (or arc length).  is the angular displacement in radians since s/r is unitless, radians are not a physical unit, and do not need to balance like most units. y x ii ff s r 

8. Relationship between angular and linear motion How fast does it go? –Angular velocity , to linear velocity, v –Direction of v is tangent to the circle –Units : v m/sec  must be in rad/s y x ii ff r v v

9. Question Two objects are sitting on a horizontal table that is undergoing uniform circular motion. Assuming the objects don’t slip, which of the following statements is true? A) Objects 1 and 2 have the same linear velocity, v, and the same angular velocity, . B) Objects 1 and 2 have the same linear velocity, v, and the different angular velocities, . C) Objects 1 and 2 have different linear velocities, v, and the same angular velocity, . D) Objects 1 and 2 have different linear velocities, v, and the different angular velocities, . 1 2

10. Question Two objects are sitting on a horizontal table that is undergoing uniform circular motion. Assuming the objects don’t slip, which of the following statements is true? A) Objects 1 and 2 have the same linear velocity, v. B) Object 1 has a faster linear velocity than object 2. C) Object 1 has a slower linear velocity than object 2. 1 2

11. Period and frequency

12. Linear vs. Circular motion: Linear motionAngular motion PositionAngle  DisplacementAngular displacement Average velocityAverage angular velocity Instantaneous velocity Instantaneous angular velocity

13. Dynamics of Uniform Circular Motion Direction: towards the center of the circle Velocity can be constant in magnitude, and we still have acceleration because the direction changes.

14. Newton’s second law Whenever we have circular motion, we have acceleration directed towards the center of the motion. Whenever we have circular motion, there must be a force towards the center of the circle causing the circular motion.

15. Dynamics of Uniform Circular Motion There is no centrifugal force pointing outward; what happens is that the natural tendency of the object to move in a straight line must be overcome. If the centripetal force vanishes, the object flies off at a tangent to the circle.

16. Dynamics of Uniform Circular Motion Example 5-11: Force on revolving ball (horizontal). Estimate the force a person must exert on a string attached to a 0.150-kg ball to make the ball revolve in a horizontal circle of radius 0.600 m. The ball makes 2.00 revolutions per second. Ignore the string’s mass.