### D C Circuits

Q- Consider the circuit in the figure. The switch is closed for long time prior to t = 0.

(a) Determine the voltage Vc across the capacitor before t = 0 and long time after t = 0

(b) Find the  expression for the voltage across the capacitor as a function of time

(c) Determine the time constant after the switch is closed

(d) Plot the voltage across capacitor for -2  < t < 5 second

Solution:

### Rotetional Motion

Q- A thin rod is held vertically with its lower end resting on a frictionless horizontal surface. The rod is then released to fall freely.

(a) Determine the speed of its center of mass just before it hits the horizontal surface. Use h, M, and g for length, mass, and gravitational acceleration respectively.

(b) Now suppose the rod has a fixed pivot at its lower end, determine the speed of the rod's center of mass just before it hits the surface.

Solution:

### 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: