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A water wheel with radius [tex]R_w[/tex] = 1.8 m and mass [tex]M_w[/tex] = 1.3 x 10³ kg is used to power a grain mill next to a river. Treat the water wheel as a hollow cylinder. The rushing water of the river rotates the wheel with a constant frequency fr = 1.4 Hz.
[tex]R_w[/tex] = 1.7m
[tex]M_w[/tex] = 17x 10³ kg
[tex]f_r[/tex] = 2.2 Hz
Calculate the angular velocity aw of the water wheel in radians/sec.

Respuesta :

Answer:

The angular velocity of the wheel is [tex]\bf{8.79~rad/s}[/tex].

Explanation:

Given:

The radius of the wheel, [tex]R_{w} = 1.8~m[/tex]

The mass of the wheel, [tex]M_{w} = 1.3 \times 10^{3}~Kg[/tex]

The angular frequency of the wheel, [tex]f = 1.4~Hz[/tex]

The angular velocity is given by

[tex]\omega = 2 \pi f\\~~~= 2 \pi (1.4~Hz)\\~~~= 8.79~rad/s[/tex]

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