An ultracentrifuge accelerates from rest to 100,000 rpm in 2.00 min. (a) what is its angular acceleration in rad/s2 ? (b) what is the tangential acceleration of a point 9.50 cm from the axis of rotation? (c) what is the radial acceleration in m/s2 and multiples of of this point at full rpm?

(a) The angular acceleration is given by:

where

is the final angular velocity

is the initial angular velocity

is the time interval

Let's convert the angular velocities in rad/s and the time in seconds:

Substituting the numbers into the equation, we find the angular acceleration:

(b) The tangential acceleration is given by the product between the angular acceleration and the distance of the point from the axis of rotation. In this case, the distance is

Therefore the tangential acceleration is

(c) The radial acceleration (also known as centripetal acceleration) is given by the product between the square of the angular velocity and the distance from the axis of rotation:

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: