A review of the basics of circular motion: The radius of a merry-go-round is 14 meters, and it takes 10 seconds to go around once. We want to calculate the speed of an atom in the outer rim. First, how far does the atom go in 12 s?

a. What is the speed of the atom?
b. What is the direction of the velocity of this atom?

In 12 s, atom goes 17.592 m distance.

(a) Speed of the atom is 8.796 m/s.

(b) The direction of the velocity of this atom is tangent to the circle.

Explanation:

Let r be the radius of the circular path and v be the speed of the atom in the outer rim.

Circumference of the circular path, d = 2πr

Substitute 14 m for r in the above equation.

Circumference of the circular path, d = 2 x π x 14 = 87.96 m

According to the problem, atom completes a revolution in 10 seconds. So, atom covers 87.96 m in 10 seconds.

Distance covered by atom in 1 second = = 8.796 m

Since, atom come back to its initial position after 10 seconds, so displacement of atom is zero. Hence,

Distance covered by atom in 12 seconds = 8.796 x 2 = 17.592 m

(a) Speed of the atom is determine by the relation :

v = =

v = 8.796 m/s

(b) In circular motion, the direction of the velocity of the atom is tangent to the the circle.  

a solenoid is created by wrapping a l = 90 m long wire around a hollow tube of diameter d = 4.5 cm.   the wire diameter is d = 0.9 mm.   the solenoid wire is then connected to a power supply so that a current of i = 9 a flows through the wire.

randomized variablesl = 90 m

d = 4.5 cm

d = 0.9 mm

i = 9 a                                          

write an expression for the number of turns, n, in the solenoid. you do not need to take into account the diameter of the wire in this calculation.

calculate the number of turns, n, in the solenoid.

write an expression for the length of the solenoid (l2) in terms of the diameter of the hollow tube d.

calculate the length of the solenoid (l2)   in meters.

calculate the magnitude of the magnetic field at the center of the solenoid in teslas.

explanation:

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