Young David who slew Goliath experimented with slings before tackling the giant. He found that he could revolve a sling of length 0.600 m at the rate of 5.00 rev/s. If he increased the length to 0.900 m, he could revolve the sling only 3.00 times per second. (a) What is the speed of the stone for each rate of rotation

Explanation:

For circular motion of stone the formula is

v = ω R where ω is angular velocity , v is linear velocity .

For first motion ,

R = length of sling = .6 m

ω = 2π n , n is no of revolution per second

ω = 2 x 3.14 x 5 = 31.4 rad /s

v = 31.4 x .6 = 18.84 m /s

For second  motion ,

R = length of sling = .9 m

ω = 2π n , n is no of revolution per second

ω = 2 x 3.14 x 5 = 31.4 rad /s

v = 31.4 x .9 = 28.26  m /s

the average speed is 24.57 km/hr

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: