A large wheel is coupled to a wheel with half the diameter as shown.
a. How does the rotational speed of the smaller wheel compare with that of the larger wheel?
b. How do the tangential speeds at the rims compare (assuming the belt doesn’t slip)?
a.
The comparison of the rotational speed of the smaller and the larger wheel shown in the given figure.
Answer to Problem 28A
Same
Explanation of Solution
Introduction:
A linear speed
Where,
Now since both the wheels are coupled using a belt, hence they will rotate with the same speed.
Conclusion:
Hence, the rotational speed of both the wheel will be same.
b.
The comparison of the tangential speed at the rims of the smaller and the larger wheel shown in the given figure.
Answer to Problem 28A
Tangential speed at the rim will be more for the larger wheel as compared to the smaller wheel.
Explanation of Solution
Introduction:
A linear speed
Where,
Since the rotational speed of both the wheels are same, thus
And, distance of the rims from the axis of rotation is larger for the larger wheel and smaller for the smaller wheel,
Thus,
Conclusion:
Hence, the larger wheel has more tangential speed at the rims as compared to the smaller wheel.
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