(hrw8c10p30) In the figure, wheel A of radius 14 cm is coupled by belt B to whee

Question

(hrw8c10p30) In the figure, wheel A of radius 14 cm is coupled by belt B to wheel C of radius 28 cm. Wheel A increases its angular speed from rest at a uniform rate of 1.6 rad/s2. Find the time for wheel C to reach a rotational speed of 150 rpm, assuming the belt does not slip. (Hint: If the belt does not slip, the linear speeds at the rims of the two wheels must be equal.)

(hrw8c10p30) In the figure, wheel A of radius 14 cm is coupled by belt B to wheel C of radius 28 cm. Wheel A increases its angular speed from rest at a uniform rate of 1.6 rad/s^2. Find the time for wheel C to reach a rotational speed of 150 rpm, assuming the belt does not slip. (Hint: If the belt does not slip, the linear speeds at the rims of the two wheels must be equal.)

Explanation / Answer

The speed of A when C is 150 RPM is 28/14 * 150 = 300.0 RPM = 300.0*2*?/60 = 31.416 rad/s. With an angular acceleration of A at 1.6 rad/s^2, the time to reach 31.416 rad/s is 40.556/1.6 s =19.635 s

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