Concept explainers
Find the angle through which the free wheel turns for each gear.
Answer to Problem 2PS
Explanation of Solution
Given information:
A bicycle’s gear ratio is the number of times the free wheel turns for every one turn of the chain wheel (see figure). The table shows the numbers of teeth in the free wheel and chain wheel for the first five gears of an
Calculation:
Here, we will consider the gear ratio bicycle. This is the number of times the free wheel turns for every one turns of the chain wheel.
We will consider the chain wheel and the free wheel attached as below:
Now, the gear numbers and the number of teeth of both the wheels are mentioned in the table below:
Now, we will consider the gear number
Thus, consider the radius of chain wheel
Now, the teeth in chain wheel are
Now, assume that the angle of rotation for free wheel is
Now, these two are same:
So, put
Hence, the angle of rotation in radian is
Now, the relation between degree and radian is:
We will convert the angle into radian:
Hence, the angle in degrees is
Now, we will consider the gear number
Thus, consider the radius of chain wheel
Now, the teeth in chain wheel are
Now, assume that the angle of rotation for free wheel is
Now, these two are same:
So, put
Hence, the angle of rotation in radian is
Now, the relation between degree and radian is:
We will convert the angle into radian:
Hence, the angle in degrees is
Now, we will consider the gear number
Thus, consider the radius of chain wheel
Now, the teeth in chain wheel are
Now, assume that the angle of rotation for free wheel is
Now, these two are same:
So, put
Hence, the angle of rotation in radian is
Now, the relation between degree and radian is:
We will convert the angle into radian:
Hence, the angle in degrees is
Now, we will consider the gear number
Thus, consider the radius of chain wheel
Now, the teeth in chain wheel are
Now, assume that the angle of rotation for free wheel is
Now, these two are same:
So, put
Hence, the angle of rotation in radian is
Now, the relation between degree and radian is:
We will convert the angle into radian:
Hence, the angle in degrees is
Now, we will consider the gear number
Thus, consider the radius of chain wheel
Now, the teeth in chain wheel are
Now, assume that the angle of rotation for free wheel is
Now, these two are same:
So, put
Hence, the angle of rotation in radian is
Now, the relation between degree and radian is:
We will convert the angle into radian:
Hence, the angle in degrees is
Chapter 4 Solutions
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