Transcript Lecture 10 - McMaster Physics and Astronomy

Circular Motion
• Newton’s Second Law and circular motion
Serway and Jewett 6.1, 6.2
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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
radial component, ac
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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).
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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
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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
radial and tangential
accelerations, and the
tension in the string?
Note: speed changes in this
case because of the
gravitational acceleration.
2
3
m
l

1
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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
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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
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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
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Designing a Road
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

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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
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Solution:
N
y

a
x
mg
 v  rg tan
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