Assume an automobile in Los Angeles is driven a total of 12,000 miles per year i

Question

Assume an automobile in Los Angeles is driven a total of 12,000 miles per year in commuting to work.

Estimate the diameter of the tire.

What is the approximate number of revolutions the car's tires undergo each year? (Use your estimate.)

A disk is initially at rest. A penny is placed on it at a distance of 1.6 m from the rotation axis. At time

t = 0 s,

the disk begins to rotate with a constant angular acceleration of

1.1 rad/s2

around a fixed, vertical axis through its center and perpendicular to its plane. Find the magnitude of the net acceleration of the coin at

t = 1.4 s.

Explanation / Answer

1 mile=5280 feet

the average circumference of the tire is
*D
or
3.14*2 feet
6.28 feet
the tire will travel 6.28 feet every revolution

12000 miles= 12000*5280 feet
revolutions = 12000*5280/6.28
10089172 revolutions

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a_tangential = (alpha) * r

where

alpha = angular acceleration

r = distance from the axis

Thus,

a_tangential = 1.76 m/s2

Now, for the radial (centripetal) acceleration,

a_radial = w2 r

To get w,

w = wo + (alpha)t

Thus, as wo = 0 (starts at rest),

w = 1.54 rad/s

Thus,

a_radial = 3.79 m/s2

Using Pythagorean theorem,

a = sqrt(a_t2 + a_r2)

Thus,

a = 4.18 m/s2   [ANSWER]

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