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A cylinder of radius 20m is rolling down with constant speed 80cm/sec what is the rotational speed

User Casademora
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The answer to this question is 0.04
User Qwertymk
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Answer:


0.04 radians per second.

Step-by-step explanation:

The circumference of this cylinder (radius
r = 20\; {\rm m}) is:


C = 2\, \pi\, r = 40\, \pi\; {\rm m}.

In other words, this cylinder will travel a linear distance of
C = 40\, \pi \; {\rm {\rm m} after every full rotation.

It is given that the cylinder rotates at a rate of
v = 80\; {\rm m\cdot s^(-1)} = 0.80\; {\rm m\cdot s^(-1)}. Thus:


\begin{aligned}\frac{0.8\; {\rm m}}{1\; {\rm s}} * \frac{1\; \text{rotation}}{40\, \pi\; {\rm m}}\end{aligned}.

Additionally, each full rotation is
2\, \pi radians in angular displacement. Combining all these parts to obtain the rotation speed of this cylinder:


\begin{aligned}\frac{0.8\; {\rm m}}{1\; {\rm s}} * \frac{1\; \text{rotation}}{40\, \pi\; {\rm m}} * \frac{2\, \pi}{1\;\text{rotation}} = 0.04\; {\rm s^(-1)}\end{aligned} (radians per second.)

User Msonsona
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