Question

A pulley of radius 10 cm turns at 6 revolutions per second. What is the linear velocity of the belt driving the pulley in meters per second?
possible answers:
376.99 m/s
1.67 m/s
166.67 m/s
3.77 m/s

Answer 1

what have you tried so far?

Answer 2

I just don't know what method to use to do this problem :l

Answer 3

angular velocity is related to linear velocity by the equation

v = wr

where v = linear velocity, w = angular velocity, and r = radius

first determine the angular velocity (how many radians does the pully travel in one second)?

hint: there are 2 pi radians in one rotation

Answer 4

An alternative (and more direct) method would be to consider exactly how many centimeters 6 rotations is.

Answer 5

Would the angular velocity be 276.001 rotations per second?

Answer 6

376*

Answer 7

Rotations?

Answer 8

the angular velocity is given at "6 revolutions per second"

Answer 9

376.991* ugh stupid keyboard

Answer 10

So then that the answer I got would be the linear velocity?

Answer 11

The circumference of this circle is

C = 2*pi*r

C = 2*pi*0.1 ... note: use 0.1 for r because 0.1 meters = 10 cm

C = 0.6283185


So if this thing is rotating 6 full rotations a second, then it's covering a linear distance of 6*0.6283185 = 3.769911 meters every second

Answer 12

btw I meant revolutions not rotations >_<

Answer 13

Okai awesome that's what I got n_n

Answer 14

I guess the best way is to imagine this thing is a wheel and you have covered the wheel with paint

then you roll the wheel out at 6 rev/sec and it will cover a linear distance of 3.769911 meters