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docker41 [41]
3 years ago
5

gives the speed v versus time t for a 0.500 kg object of radius 6.00 cm that rolls smoothly down a 30° ramp. The scale on the ve

locity axis is set by vs = 4.0 m/s. What is the rotational inertia of the object?

Physics
1 answer:
ddd [48]3 years ago
8 0

Answer:

Rotational inertia of the object is given as

I = 7.2 \times 10^{-4} kg m^2

Explanation:

As we know that the acceleration of the object on inclined plane is given as

a = \frac{gsin\theta}{1 + k^2/R^2}

now we know that velocity at any instant of time is given as

v = at

now we know that if the graph between velocity and time is given then the slope of the graph will be same as acceleration

so here we have

\frac{gsin\theta}{1 + k^2/R^2} = slope

now from the graph slope of the graph is given as

slope = \frac{3.5 - 0}{1}

\frac{gsin\theta}{1 + k^2/R^2} = 3.5

\frac{9.81 sin30}{1 + k^2/R^2} = 3.5

k^2 = 0.4 R^2

now rotational inertia is given as

I = mk^2

I = 0.5(0.4)(0.06)^2

I = 7.2 \times 10^{-4} kg m^2

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