1     If 2π radians equals 360°, calculate the number of degrees in one radian.

 

2     Calculate the angular velocity in rad s^-1 of the second hand of an analogue watch.

 

3     The graph below shows the variation of angular velocity with time for a rotating        body.

 

                           

 (a) Find the angular displacement covered in the first 3 seconds.

(b) Find the total angular displacement for the 6 seconds.

(c) Calculate the angular acceleration of the rotating body.

 

4     A wheel accelerates uniformly from rest.  After 12 s the wheel is completing 100 revolutions per minute (r.p.m.)

(a) Convert 100 r.p.m. to its equivalent value in rad s^-1.

(b) Calculate the average angular acceleration of the wheel.

 

5    The angular velocity of a car engine’s drive shaft is increased from 100 rad s^-1 to 300 rad s^-1 in 10 s.

(a) Calculate the angular acceleration of the drive shaft.

(b) Calculate the angular displacement during this time.

(c) A point on the rim of the drive shaft is at a radius of 0.12 m.

Calculate the distance covered by this point in the 10 s time interval.

 

6     Use calculus methods to derive the equations for angular motion.  The method is very similar to that for linear motion.

Note: in the unit or course assessment you may be asked to derive the linear motion equations but not the angular motion equations.