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.

Solution:

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.

Solution:

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

Solution:

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?

Solution:

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.

Solution::