Lecture 16 Friday, October 3 Chapter 6: Circular Motion

Review Example Macie pulls a 40 kg rolling trunk by a strap angled at 30° from the horizontal. She pulls with a force of 40 N, and there is a 30 N rolling friction force acting on trunk. What is the trunk’s acceleration? Slide 5-17

For uniform circular motion, the acceleration 1.Is parallel to the velocity 2.Is directed towards the center of the circle 3.is larger for a larger orbit at the same speed

Problem, interacting bodies Glider on a air track Massless, frictionless pulley m1m1 m2m2

Special Assignment Special assignment to be handed in Monday: Workbook pages 4-5 and 4-6, exercises and page 5-5, exercises

The kinematics of uniform circular motion The dynamics of uniform circular motion Circular orbits of satellites Newton’s law of gravity Chapter 6 Circular Motion, Orbits and Gravity Topics: Sample question: The motorcyclist in the “Globe of Death” rides in a vertical loop upside down over the top of a spherical cage. There is a minimum speed at which he can ride this loop. How slow can he go? Slide 6-1

Uniform Circular Motion Uniform magnitude of velocity (speed) is constant

Circular Motion Note similarity to the equations for one- dimensional linear motion

Going from angular velocity to angular displacement:

UCM continued Travelling at constant speed v around circle Period is time one around circle = T

UCM cont s is distance travelled around circumference and the definition of the radian tell us

Uniform Circular Motion Uniform magnitude of velocity (speed) ω, is constant But α is not zero because direction of velocity is changing.

Uniform Circular Motion Slide 6-13

Newton’s Second Law Net force must point towards center of circle

Example A level curve on a country road has a radius of 150 m. What is the maximum speed at which this curve can be safely negotiated on a rainy day when the coefficient of friction between the tires on a car and the road is 0.40? Slide 6-24

Top View v

When a ball on the end of a string is swung in a vertical circle: What is the direction of the acceleration of the ball? A.Tangent to the circle, in the direction of the ball’s motion B.Toward the center of the circle Checking Understanding Slide 6-11

Problems due today 5: 24, 25, 29, 30, 31, 35, 36, 37, 39