A water wheel with radius R_w = 1.8 m and mass M_w = 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…

Question

A water wheel with radius
`R_w` = 1.8 m and mass
`M_w` = 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.


`R_w` = 1.7m

`M_w` = 17x 10³ kg

`f_r` = 2.2 Hz
Calculate the angular velocity aw of the water wheel in radians/sec.

Answer 1

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

Step-by-step explanation:

Given:

The radius of the wheel,
`R_(w) = 1.8~m`

The mass of the wheel,
`M_(w) = 1.3 * 10^(3)~Kg`

The angular frequency of the wheel,
`f = 1.4~Hz`

The angular velocity is given by

`\omega = 2 \pi f\\~~~= 2 \pi (1.4~Hz)\\~~~= 8.79~rad/s`