Check the following for correctness please?

Question

A pulley of radius 20 cm turns at 6 revolutions per second, what is the linear velocity of the belt driving the pulley in meters per second?

Is 753.98m/s the solution?

Thank you for the help Rec.

Answer 1

ω = 6 x 2π radians / s
ω = 12 π radians / s
v = ω r
v = 12 π x 20 cm / s
v = 240 π cm / s
v = 7.54 m / s

Answer 2

it turns 6 rel/sec or 6 perimeters/sec

the perimeter of the pulley is 40pi cm

so 6 perimeters of 40pi will be 6 * 40pi = 240pi cm

so the linear speed in cm/s is 240pi cm/s

we know 100cm = 1m

240pi cm/s = 2.4pi m/s or about 7.536 m/s


Rec