A2.10 kg textbook rests on a frictionless, horizontal surface. a cord attached to the book passes over a pulley whose diameter is 0.170 m, to a hanging book with mass 3.00 kg. the system is released from rest, and the books are observed to move 1.20 m in 0.900 s.
(a) what is the tension in each part of the cord?
(b) what is the moment of inertia of the pulley about its rotation axis?

(A) 6.2 N and 20.52 N

(B) I = 0.035 kg m^{2}

Explanation:

mass of first book (M1) = 2.1

mass of second book (M2) = 3 kg

diameter of pulley = 0.17 m

distance (s) = 1.2 m

time = 0.9 secs

(A) what is the tension in each part of the cord

    we first have to get the acceleration of the first  book

 s = ut + 0.5 at^{2}

 since the books are initially at rest u = 0

s = 0.5 at^{2}

1.2 = 0.5 x a x 0.9^{2}

a = 2.96 m/s^[2}

       T1 = 2.1 x 2.96 = 6.2 N

          (g-a) is the net acceleration of the first book

           T2 = 3 x ( 9.8 - 2.96 ) = 20.52 N

(B) What is the moment of inertia of the pulley?

     taking clockwise rotation of the pulley to be negative while

     anticlockwise to be positive, we can see from the diagram that T1      

     causes a clockwise rotation while T2 produces an anticlockwise rotation

       ( T2 - T1 )r = I∝

         where ∝ is the angular acceleration of the pulley relative to its radial  

         acceleration, ∝ = \frac{a}{r}

          ( T2 - T1 )r = I\frac{a}{r}

          I = \frac{(T2 - T1)r^{2}}{a}

          I = \frac{(20.52 - 6.2)0.085^{2}}{2.96}

         I = 0.035 kg m^{2}

answer: the direction of the wind is expressed as the direction from which the wind is blowing. for example, easterly winds blow from east to west, while westerly winds blow from west to east.

explanation:

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: