Two pulleys are connected by a belt that goes over the rim of each. One pulley has a radius of 35cm and rotates at 425 rpm. The other...?

Question

Two pulleys are connected by a belt that goes over the rim of each. One pulley has a radius of 35cm and rotates at 425 rpm. The other pulley is rotating at 700 rpm. Find the linear velocity of the belt in cm/sec, and the radius of the second pulley.

only use v=rw

Answer 1

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v = rω

v = 35 cm(425 rev/min (2π radian/rev) / (60 s/min))

v = 1557.706... ≈ 1560 cm/s  ◄

              v = rω

1557.706 = r(700 rev/min (2π radian/rev) / (60 s/min))

              r = 0.2125 m ≈ 21¼ cm   ◄

Answer 2

425 rev/min x 1 min/60s  = 7.083 rev/s

1 rev = 1 circumference = 70π cm

70π cm/rev x 7.083 rev/s = 1558 cm/s (linear speed of first pulley and second pulley and belt)

for second pulley, assuming belt is not slipping.

R = radius

1 rev = 1 circumference = 2πR cm

700 rpm x 1 min/60s  = 11.67 rev/s

11.67 rev/s x 2πR cm/rev = 73.30(R) cm/s

1558  =  73.30(R)

R = 21.2 cm