Each roller under a conveyor belt has a radius of 0.5 meters. the rollers turn at a rate of 30 revolutions per minute. what is the linear velocity of the conveyor belt?

The linear velocity of the conveyor belt is v=0.25 m/s.

Explanation:

In a circular motion, the tangential velocity can be written as

where r is the radius of the circle, and ω is the angular velocity.

In this case, we were given some data: the radius r=0.5 meters, and the revolutions per minute of the rollers. The first thing we have to do is to calculate ω with the proper units, which is rad/second, using the given revolutions per minute, so

because in 1 minute, there are 60 seconds, and in 1 revolution, there are 2π rad.

Now, we can calculate the

in which we had to convert rad/s to Hz (or 1/s), knowing that 2πrad=1Hz.

Therefore, the answer is v=0.25 m/s.

two charges are fixed in place on the x-axis as shown. the charge at x = 0 is negative and has magnitude q = 2 μcoulombs (1 μcoulomb = 10-6 coulombs). the charge at x = d, (d = +12 cm), is positive and has magnitude q = 4 μcoulombs. find a point x = xo along the x-axis at which the electric field is zero.

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