Circular Motion

Uniform Circular Motion Period (T) = time to travel around circular path once. (C = 2 πr). Speed is constant, VELOCITY is NOT. Direction of the velocity is ALWAYS changing. We call this velocity, TANGENTIAL velocity as its direction is TANGENT to the circle.

Centripetal Acceleration  vv vv Centripetal means “center seeking” so that means that the acceleration points towards the CENTER of the circle. v v θ

Drawing the Directions correctly So for an object traveling in a counter-clockwise path. The velocity would be drawn TANGENT to the circle and the acceleration would be drawn TOWARDS the CENTER. To find the MAGNITUDES of each we have:

Circular Motion and N.S.L Recall that according to Newton’s Second Law, the acceleration is directly proportional to the Force. If this is true: NOTE: The centripetal force is a NET FORCE. It could be represented by one or more forces. So NEVER draw it in an FBD.

Examples The blade of a windshield wiper moves through an angle of 90 degrees in 0.28 seconds. The tip of the blade moves on the arc of a circle that has a radius of 0.76m. What is the magnitude of the centripetal acceleration of the tip of the blade?

Examples What is the minimum coefficient of static friction necessary to allow a penny to rotate along a 33 1/3 rpm record (diameter= m), when the penny is placed at the outer edge of the record? mg FNFN FfFf Top view Side view

Satellites in Circular Orbits Consider a satellite travelling in a circular orbit around Earth. There is only one force acting on the satellite: gravity. Hence, FgFg There is only one speed a satellite may have if the satellite is to remain in an orbit with a fixed radius.

Examples Venus rotates slowly about its axis, the period being 243 days. The mass of Venus is 4.87 x kg. Determine the radius for a synchronous satellite in orbit around Venus. (assume circular orbit) FgFg 1.54x10 9 m

Welcome Today, Mr. Souza will give some notes about banked curves and vertical circular motion. You may Sit in the first several rows in order to join the discussion about the above two topics OR Sit towards the back part of the room and begin work on tonight’s homework:  C&J p.150 # 21, 24, 26, 35, 36, 37, 40, 42

Banked Curves FNFN W=mg θ θ F N cos(θ) F N sin(θ) A car of mass, m, travels around a banked curve of radius r.

Banked Curves Example Design an exit ramp so that cars travelling at 13.4 ms -1 (30.0 mph) will not have to rely on friction to round the curve (r = 50.0 m) without skidding. W=mg θ θ F N cos(θ) F N sin(θ) FNFN

Vertical Circular Motion mg NTNT NRNR NLNL NBNB What minimum speed must she have to not fall off at the top? Gratuitous Hart Attack

What minimum speed must she have to not fall off at the top? Vertical Circular Motion mg NTNT

Examples The maximum tension that a 0.50 m string can tolerate is 14 N. A 0.25-kg ball attached to this string is being whirled in a vertical circle. What is the maximum speed the ball can have (a) at the top of the circle, and (b)at the bottom of the circle? mg T (a)

Examples (b) At the bottom? mg T

Homework C&J p.150 # 21, 24, 26, 35, 36, 37, 40, 42 Please watch these two video clips (they relate to problem #37).   Homework problems and links to video clips will be posted on Mr. Souza’s ASD site.