Circular Motion Newtons Second Law and circular motion

Circular Motion • Newton’s Second Law and circular motion Serway and Jewett 6. 1, 6. 2 Physics 1 D 03 - Lecture 10 1

Review: Circular Motion Kinematics has components center tangential component, radial component, Physics 1 D 03 - Lecture 10 2

Particle dynamics : nothing new • There is no “centrifugal force” • • has a radial component as well as (perhaps) a tangential component Centrifugal Force Centrifugal force is a fictitious force – it is the result of you being in a non-inertial (accelerating) frame (see Sect 7. 5). Physics 1 D 03 - Lecture 10 3

Example: Pendulum Calculate the tension in the string when the pendulum is at the lowest point in the swing. Given : mass m, length L, and speed at the lowest point. L m m Physics 1 D 03 - Lecture 10 4

Non-Uniform Circular Motion Suppose a pendulum is moving fast enough that it swings in a complete vertical circle. Assume we know the mass m, length l, and the speeds at each point. How do we calculate the radial and tangential accelerations, and the tension in the string? Note: speed changes in this case because of the gravitational acceleration. 2 3 l m 1 Physics 1 D 03 - Lecture 10 5

Concept Quiz The earth is not exactly spherical, so the gravitational field g depends on latitude. The rotation of the earth also affects the measurement of “weight. ” A physicist owns a bathroom scale which reads in newtons. He travels to the North Pole, where the scale reads 978 N when he stands on it. If the earth were to spin twice as fast, what would the bathroom scale read at the pole? rotation a) 978 N b) less than 978 N c) greater than 978 N Physics 1 D 03 - Lecture 10 6

Concept Quiz The earth is not exactly spherical, so the gravitational field g depends on latitude. The rotation of the earth also affects the measurement of “weight. ” The same physicist travels with his bathroom scale to the equator, where the scale reads 978 N when he stands on it. The gravitational force on him at the equator is: rotation a) equal to 978 N b) less than 978 N c) greater than 978 N Physics 1 D 03 - Lecture 10 7

Example : How fast can the car go without sliding? Friction of the road on the tires provides the force needed to keep the car traveling in a circle. If the road is icy (no friction) the car travels in a straight line. r Physics 1 D 03 - Lecture 10 8

Designing a Roads are “banked” – tilted from side to side on curves – to allow cars to travel at higher speeds without sliding off. Q: At what speed can the car follow the road with no friction? Q: What does the free-body diagram look like at other speeds? r r Physics 1 D 03 - Lecture 10 9

Example: Calculate the speed at which the car can negotiate the curve without friction. Assume constant speed. Free-body diagram: - Two forces: N and gravity is horizontal, since the circular path is horizontal. - the horizontal component of N is the “centripetal” force Physics 1 D 03 - Lecture 10 10

N Solution: y x mg Physics 1 D 03 - Lecture 10 11