In the figure, wheel A of radius r A = 14.6 cm is coupled by belt B to wheel C o

Question

In the figure, wheel A of radius rA = 14.6 cm is coupled by belt B to wheel C of radius rC = 20.4 cm. The angular speed of wheel A is increased from rest at a constant rate of 1.86 rad/s2. Find the time needed for wheel C to reach an angular speed of 77.4 rev/min, assuming the belt does not slip. (Hint: If the belt does not slip, the linear speeds at the two rims must be equal.)

In the figure, wheel A of radius rA = 14.6 cm is coupled by belt B to wheel C of radius rC = 20.4 cm. The angular speed of wheel A is increased from rest at a constant rate of 1.86 rad/s2. Find the time needed for wheel C to reach an angular speed of 77.4 rev/min, assuming the belt does not slip. (Hint: If the belt does not slip, the linear speeds at the two rims must be equal.)

Explanation / Answer

Here ,

as aA = 1.86 rad/s^2

rA = 14.6 cm

rC = 20.4 cm

As , for belt not slipping

aA * rA = aB * aB

1.86 * 14.6 = 20.4 * aC

aC = 1.33 rad/s^2

Now , as the final angular speed of C ,wC = 77.4 rev/min

wC = 8.1 rad/s

Using first equation of motion ,

wf = wi + a*t

8.1 = 1.33 * t

t = 6.09 s

the time taken for c to reach 77.4 rev/min is 6.09 s

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