Linear Motion Combined with Rotaional Motion

Q- A m1 = 16.0 kg object and a m2 = 12.5 kg object are suspended, joined by a cord that passes over a pulley with a radius of 10.0 cm and a mass of 3.00 kg. The cord has a negligible mass and does not slip on the pulley. The pulley rotates on its axis without friction. The objects start from rest 3.00 m apart vertically. Treating the pulley as a uniform disk, determine the speeds of the two objects as they pass each other.


EMI: Induced Current

Q-Two parallel circular loops of wire having the same common axis.  The smaller loop of radius r, and is above the larger loop (radius R) by a distance X>>R.  the magnetic field due to the counterclockwise current i in the larger loop is nearly uniform throughout the smaller loop.  Suppose that x is increasing at a constant rate dx/dt = v.  

(a) Find the expression for the magnetic flux through the area of the smaller loop as a function of x.

(b) In the smaller loop, find the expression for the induced emf and the direction of the induced current.


Circular Motion

(Requested by Tricky Bits)

Q- A wheel 1.9 m in diameter lies in a vertical plane and rotates about its central axis with a constant angular acceleration of 4.15 rad/s2. The wheel starts from rest at t = 0, and the radius vector of a certain point P on the rim makes an angle of 57.3o with the horizontal at this time. At t = 2.00 s, find the following.

a) The angular speed to the wheel

b) The tangential speed of the point P

c) The total acceleration of the point P (magnitude and direction)

d) The angular position of the point P


Conservation of Energy: Motion in Vertical Plane

Q- A pendulum consists of a string of length L and a bob of mass M.  The string is brought to a horizontal position and given the minimum initial speed enabling a pendulum to make a full turn in the vertical plane.  

a) what is the maximum kinetic energy K of the bob? 

b) what is the tension in the string when the kinetic energy is maximum?


Electrostatics: Capacitance

Q- Five 1 inch square plates are arranged as shown in figure. The plate spacings are 0.01 inch. The arrangement is to be used for a displacement transducer by observing the change in capacitance with the distance x. Calculate the sensitivity of the device in picofarads per inch. Assume that the plates are separated by air. 


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