(a) The capacitance of the capacitor is:

and the voltage applied across its plates is

The relationship between the charge Q on each plate of the capacitor, the capacitance and the voltage is:

and re-arranging it we find the charge stored in the capacitor:

(b) The electrical potential energy stored in a capacitor is given by

where C is the capacitance and V is the voltage. The new voltage is

so the energy stored in the capacitor is
To solve this problem it is necessary to apply the concepts related to rotational kinetic energy, the definition of the moment of inertia for a sphere and the obtaining of the radius through the circumference. Mathematically kinetic energy can be given as:

Where,
I = Moment of inertia
Angular velocity
According to the information given we have that the radius is



With the radius obtained we can calculate the moment of inertia which is



Finally, from the energy equation and rearranging the expression to obtain the angular velocity we have to



Therefore the angular speed will the ball rotate is 25.95rad/s
The cyclist is moving by uniformly accelerated motion, with an initial velocity of

and an acceleration of

.
The acceleration is given by

where

is the final velocity and

is the time between the end and the beginning of the motion, and in our case it is 1.75 s. Therefore, from this relationship we can find the final velocity: