Task $1.$

A hill test is being carried out $-$ the motorcycle and test$-$rider have an all$-$up mass of $400$ kg $.$ The wheels each have a mass of $25$ kg $,$ diameter of $550$ mm and radius of gyration of $250$ mm $.$ The motorcycle accelerates from rest to $30\frac{m}{s}$ over a distance of $150$ m $,$ whilst climbing a hill of slope $1$ in $25.$ The average resistance to motion, including drag, is $150$ N $.$

Identify all the energy changes required in the calculation and explain why they are necessary, then calculate:

a$.$ The total work done as the motorcycle ascends the incline.

b$.$ The power developed during the climb.

At another point in its journey, the motorcycle and rider travel at $70k\frac{m}{h}$ around a lefthand bend of radius $50$ m $.$ Calculate:

c$.$ The angular velocity of each wheel.

d$.$ The moment of inertia of each wheel.

e$.$ The size and effect of the gyroscopic torque produced on the bike.