Uniform Circular Motion Chapter 5 Lesson 1

5.1 Uniform Circular Motion Object is traveling at a constant (uniform) speed on a circular path Period (T) – Time it takes to make one trip around the circle Circumference – distance around the circle C = 2r

Uniform Circular Motion Speed (v) – distance / time Find v v = 3.77 m/s 1.2 m Work on board v = 2r / T  v = 2(1.2m)/2s  v = 2.4m /2s = 3.77 m/s T=2s

Uniform Circular Motion Speed is constant Velocity is not constant Velocity is always changing This acceleration is “centripetal” acceleration

5.2 Centripetal Acceleration Object moves in circular path At time t0 it is at point O with a velocity tangent to the circle At time t, it is at point P with a velocity tangent to the circle The radius has moved through angle 

Centripetal Acceleration Draw the two velocity vectors so that they have the same tails. The vector connecting the heads is v Draw the triangle made by the change in position and you get the triangle in (b)

Centripetal Acceleration Since the triangles have the same angle are isosceles, they are similar

Centripetal Acceleration

Centripetal Acceleration Know this

Centripetal Acceleration At any given moment v is pointing tangent to the circle ac is pointing towards the center of the circle If the object suddenly broke from circular motion would travel in line tangent to circle Have a string with something soft on end. Swing it and let go to illustrate.

Example 1 Two identical cars are going around two corners at 30 m/s. Each car can handle up to 1 g. The radius of the first curve is 50m and the radius of the second is 100 m. Do either of the cars make the curve? (hint find the ac) Yes, 100m ac1 = v2/r  ac1 = (30 m/s)2/50m  ac1 = 18 m/s2 Can’t make it ac2 = (30 m/s)2/100m = 9 m/s2 Yes 50 m 100 m

Example 5-1 A 150 kg ball at the end of a string is revolving uniformly in a horizontal circle of radius 0.600 m. The ball makes 2.00 revolutions in a second. What is its centripetal acceleration?

Example 5-2 The moon’s nearly circular orbit about the earth has a radius of about 384,000 km and a period T of 27.3 days. Determine the acceleration of the moon toward the earth.

What is Centripetal Force?

5-2 Dynamics of Uniform Circular Motion For an object to be in uniform circular motion, there must be a net force acting on it. We already know the acceleration, so can immediately write the force: (5-1) We can see that the force must be inward by thinking about a ball on a string:

Directions in centripetal force problems: Positive direction is inwards toward center of circle. Negative direction is outward away from center of circle.

5-2 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 tangent to the circle.

Example 5-3 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 (T=0.500 s).

To Be Continued…