1) State the work-kinetic energy theorem with friction forceacting on the system ?

2) For a rigid object undergoing circular motion, show that thetangential acceleration for each point on the object is given by ??= ??.?

3) A particle starts from the origin with velocity 5 ?̂m/s at t= 0 and moves in the xy plane with a varying acceleration given by?⃗ = (2? ?̂+ 6√? ?̂), where ?⃗ is in meters per second squared andt is in seconds.

i) Determine the velocity of the particle as a function of time.?

ii) Determine the position of the particle as a function of time?

4)John is riding a bicycle and comes across a hill of height7.30 m. At the base of the hill, he is traveling at 6.00 m/s. Whenhe reaches the top of the hill, he is traveling at 1.00 m/s.Jonathan and his bicycle together have a mass of 85.0 kg. Ignorefriction in the bicycle mechanism and between the bicycle tires andthe road.

i) What is the total external work done on the system ofJonathan and the bicycle between the time he starts up the hill andthe time he reaches the top ?

ii) What is the change in potential energy stored in Jonathan’sbody during this process?

5) A flywheel has a moment of inertia of 1.6 × 10−3 kg.m2 . Whena constant torque is applied, it reaches an angular velocity of1200 rev/min in 15 s. Assuming it started from rest, find:

i) the angular acceleration ?

ii) the unbalanced torque applied ?

iii) the angle turned through 15 s ?

iv) the work done on the flywheel by the torque ?