# Lecture 10 - McMaster Physics and Astronomy

```Circular Motion
• Newton’s Second Law and circular motion
Serway and Jewett 6.1, 6.2
Physics 1D03 - Lecture 10
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Review: Circular Motion Kinematics

a has components

dv
i) at 
, rate of change of spe e d
dt
v2
ii) ac 
, from changein direction
r

a
center
tangential component, at
Physics 1D03 - Lecture 10
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Particle dynamics : nothing new
• There is no “centrifugal force”

•  (real forces)  ma

• a 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 1D03 - Lecture 10
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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

vo
Physics 1D03 - Lecture 10
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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
accelerations, and the
tension in the string?
Note: speed changes in this
case because of the
gravitational acceleration.
2
3
m
l

1
Physics 1D03 - Lecture 10
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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 1D03 - Lecture 10
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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 1D03 - Lecture 10
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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.

v

a

fs
r
Physics 1D03 - Lecture 10
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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 1D03 - Lecture 10
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Example:
Calculate the speed at which the car can negotiate
the curve without friction. Assume constant speed.
Free-body diagram:

N

a
- Two forces: N and
gravity

- a is horizontal, since the
circular path is horizontal.
- the horizontal component
of N is the “centripetal”
force

mg
Physics 1D03 - Lecture 10
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Solution:
N
y

a
x
mg
 v  rg tan
Physics 1D03 - Lecture 10
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