101: Physics Lecture 08
Exam 2
Circular Motion and Centripetal Acceleration
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Todays lecture will cover Chapter 5
Physics 101: Lecture 8, Pg 1
Circular Motion Act
B A C
A ball is going around in a circle attached to a string. If the string breaks at the instant shown, which path will the ball follow? Physics 101: Lecture 8, Pg 2
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Acceleration in Uniform Circular Motion
v2 R R v1 v v2 v1
v2 a= R
centripetal acceleration
aave= v / t
Acceleration inward
Acceleration is due to________________________ __________________________________________.
Physics 101: Lecture 8, Pg 3
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ACT
Consider the following situation: You are driving a car with constant speed around a horizontal circular track. On a piece of paper, draw a Free Body Diagram (FBD) for the car. How many forces are acting on the car? A) 1 B) 2 C) 3 D) 4 E) 5
The net force on the car is A. Zero B. Pointing radially inward C. Pointing radially outward
Physics 101: Lecture 8, Pg 4
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ACT
Suppose you are driving through a valley whose bottom has a circular shape. If your mass is m, what is the magnitude of the normal force FN exerted on you by the car seat as you drive past the bottom of the hill A. FN < mg B. FN = mg C. FN > mg R
v
Physics 101: Lecture 8, Pg 5
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Roller Coaster Example
What is the minimum speed you must have at the top of a 20 meter roller coaster loop, to keep the wheels on the track.
Y Direction: F = ma
Physics 101: Lecture 8, Pg 6
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Circular Motion
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Angular displacement = 2-1 How far it has rotated Angular velocity = /t How fast it is rotating Units radians/second 2 = 1 revolution Period =1/frequency T = 1/f = 2 / Time to complete 1 revolution 101: Lecture 8, Pg 7 Physics
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Circular to Linear
l Displacement l Speed
s = r ( in radians)
|v| = s/t = r /t = r of v is tangent to circle
l Direction
Physics 101: Lecture 8, Pg 8
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Merry-Go-Round ACT
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Bonnie sits on the outer rim of merry-go-round a with radius 3 meters, and Klyde sits midway between the center and the rim. The merry-go-round makes one complete revolution every two seconds. Klyde Bonnie Klydes speed is:
(a) the same as Bonnies (b) twice Bonnies (c) half Bonnies
Physics 101: Lecture 8, Pg 9
Merry-Go-Round ACT II
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Bonnie sits on the outer rim of a merry-go-round, and Klyde sits midway between the center and the rim. The merry-goround makes one complete revolution every two seconds. Klydes angular velocity is:
Klyde Bonnie
(a) the same as Bonnies (b) twice Bonnies (c) half Bonnies
Physics 101: Lecture 8, Pg 10
Angular Acceleration
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Angular acceleration is the change in angular velocity divided by the change in time.
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If the speed of a roller coaster car is 15 m/s at the top of a 20 m loop, and 25 m/s at the bottom. What is the cars average angular acceleration if it takes 1.6 seconds to go from the top to the bottom?
f 0 t
Physics 101: Lecture 8, Pg 11
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Summary
(with comparison to 1-D kinematics)
Angular
= constant
Linear
a = constant
= 0 + t
1 2 = 0 + 0 t + t 2
v = v 0 + at
x = x0 + v 0 t +
1 2 at 2
And for a point at...