Jonathan is riding a bicycle and encounters a hill of height h. At the base of the hill, he is traveling at a speed vi . When he reaches the top of the hill, he is traveling at a speed vf . Jonathan and his bicycle together have a mass m. Ignore friction in the bicycle mechanism and between the bicycle tires and the road. (a) What is the total external work done on the system of Jonathan and the bicycle between the time he starts up the hill and the time he reaches the top? (b) What is the change in potential energy stored in Jonathans body during this process? (c) How much work does Jonathan do on the bicycle pedals within the Jonathan bicycleEarth system during this process?

Rotational Kinematics and Energy Rotational Kinematics ● A relationship exists between linear and angular quantities. To do this all angles have to be measured in radians. ● Analogies: ○ Linear Angular Position x (position) θ (radians) Velocity v (velocity) ω(angular velocity) Acceleration a (acceleration) α(angular acceleration) Force F (force) τ (torque) Mass m (mass) I (moment of inertia) ○ ○ COUNTERCLOCKWISE IS POSITIVE