Periodic time (T) is the time taken for one complete revolution, cycle or oscillation.
PERIODIC TIME AND ANGULAR VELOCITY
T 2p v
T periodic time v angular velocity
PERIODIC TIME AND LINEAR VELOCITY
T 2pr v
T periodic time v linear velocity r radius of rotation
r = radius of rotation
The orbital period (T ) is the time taken for a given object to make one complete orbit about another object.
In the case of the period of an orbit, we can calculate periodic time from the definition of angular velocity
t is the period (T).
v t
, given that the angle is a full revolution (2) and the time
v t Qv 2p
T QT 2p v Periodic time can also be related to linear velocity as .
T 2pr v
Centripetal Acceleration CENTRIPETAL ACCELERATION
Centripetal acceleration is the acceleration of an object travelling in uniform circular motion; it is directed toward the centre of the circle.
v a CENTRIPETAL ACCELERATION
Fig 6.2: Particle in circular motion, directions of velocity and acceleration shown
a 2r a acceleration, angular velocity, r radius or
a acceleration, v linear velocity, r radius a v2
r SAMPLE PROBLEM 6B
A discus thrower is spinning is such a way that his discus is travelling in a circular path at a constant speed of 22 m s1. He has an arm span of 2.06 m. Calculate the centripetal acceleration of the discus.You may assume that the discus is at the very edge of his hand.
1Proof is on the website www.gillmacmillan i.e. for illustrative purposes as it is not subject to examination. 100 INVESTIGATING PHYSICS
As with any acceleration, it’s a vector quantity with an SI unit of metres per second squared (m s2.)
It can be proven1 that centripetal acceleration is directed towards the centre of the object’s circular path and has a magnitude given by the equations:
