Physics 121

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Physics 121
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5. Kinematics in 2-D and Vectors
5.1 Kinematics of Uniform Circular Motion 5.2
Dynamics of Uniform Circular Motion 5.3 A Car
Rounding a Curve 5.6 Newtons Law of Universal
Gravitation 5.7 Gravity near the Earths
Surface 5.8 Satellites and Weightlessness
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Example 5.1 . . . Round and round
A red car goes counterclockwise around a track at
a constant speed (see figure)
A. The car is accelerating and Q shows the
direction of the force on it B. The car is
accelerating and P shows the direction of the
force on it C. The car is not accelerating D. The
car is accelerating but there is no force acting
on it.
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Solution 5.1 . . . Round and round
A. The car is accelerating and Q shows the
direction of the force on it.

• Centripetal Force changes the direction
• Centripetal Force does not change speed
• Centripetal Force points toward the center

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Example 5.2 . . . Centripetal Force Equation
The correct equation for centripetal force is A.
F mv B. F mvr C. F mv / r D. F mv2 / r
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Solution 5.2 . . . Centripetal Force Equation

• The correct equation for centripetal force is
• F mv2 / r

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Example 5.3 . . . Centripetal Acceleration
The correct equation for centripetal acceleration
is A. a mvr B. a vr C. a v / r D. a
v2 / r
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Solution 5.3 . . . Centripetal Acceleration
The correct equation for centripetal acceleration
is D. a v2 / r
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Example 5.4 . . . Stoned and Strung
Dennis the menace ties a 250 g rock to a 160
cm. string and whirls it above his head. The
string will break if the tension exceeds 90 N.
What minimum speed will endanger the windshield
on his neighbors car?
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Solution 5.4 . . . Stoned and Strung
Centripetal Force is F mv2 / r 90 (0.25)(v2
/ 1.6 ) v 24 m/s
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Example 5.5 . . . Slippery when wet!
A car exits on a ramp (unbanked) of radius 20 m.
The coefficient of friction is 0.6. The maximum
speed before slipping starts is most nearly A.
10 m/s B. 20 m/s C. 40 m/s D. 120 m/s
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Solution 5.5 . . . Slippery when wet!
Force of Friction Centripetal
force (0.6)(m)(g) (m)(v2) / r v 11 m/s
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Is there gravity on Mars?

• Newton's Law of Universal Gravitation
• F GmM/r2
• Compare with F mg so
• g GM/r2
• g depends inversely on the square of the distance
• g depends on the mass of the planet
• g on the Moon is 1 /6 of g on Earth

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Example 5.6 . . . A Neutron Stars Gravity
An exotic finish to massive stars is that of a
neutron star, which might have as much as five
times the mass of our Sun packed into a sphere
about 10 km in radius! Estimate the surface
gravity on this monster.
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Solution 5.6 . . . A Neutron Stars Gravity
g GM/r2 g (6.67x10-11)(5x1.99x1030) /
(104)2 g 6.7x 1012 m/s2
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Example 5.7 . . . Satellites
Geosynchronous satellites are used for cable TV
transmission and weather forecasting. They orbit
about 36,000 km above the Earths surface. This
is six times the radius of the Earth which is
6,000 km. What is the value of g at that
height?
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Solution 5.7 . . . Satellites
The distance of the satellite from the center of
the Earth is 7 RE so the acceleration due to
gravity must be 1 / 49 that on the surface of the
Earth. (1/49)(9.8) 0.2 m/s2
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Thats all folks!