Definition
Average angular acceleration,αav is defined as the rate of change of angular velocity.
Where:
ω2: final angular velocity
ω2: final angular velocity
ω1: initial angular velocity
∆t:time interval
average angular velocity,ωav
definition:
average angular velocity,ωav is defined as the rate of change of angular displacement
where:
Ɵ2:final angular displacement in radian
Ɵ1:initial angular4 displacement in radian
∆t:time interval
Example 2 :
express (a) 100 revolutions per minute (rpm) in rad s-1
(b)25 rad s-1 in revolution per second
Solution:1rev=2ᴨ rad and 1 rpm =
(a) 100 rpm→rad s-1
1st method;
100 rpm= X X =10.47rad s-1
2nd method;
100 rpm=100X rad s-1 = 10.47 s-1
Example 3 :
If the angular the displacement,Ɵ of rotating wheel is given by
Ɵ=2Π+
Determine,
I. the average angular velocity at time t1=3.0 s and t2=5.0 s
II. instantaneous angular velocity at time t=5.0 s
Angular acceleration is the vector of quantity. The unit of angular acceleration is the rads. If the angular acceleration α, is the positive then the angular velocity ω, is increasing. If the angular acceleration α,is the negative then the angular velocity ω,is decreasing.Angular acceleration
2.instantaneous angular acceleration,α
Definition:
Instantaneous angular acceleration is defined as the instantaneous rate of change of angular velocity.
Example 4:
The instantaneous angular velocity,ω of the bicyle wheel is given by
ω =6t3+2t2
calculate,
a.the instantaneous angular velocity at time,t = 2.0 s
Instantaneous angular velocity,ω=6t3=2t2
a) ω at time,t=2.0 s
ω=6t3+2t2=6(2)3+2(2)2=56 rad s-1
at time,t=2.0 s
ω1=6(2.0)3+2(2.0)2→ω1=56 rad s-1
at time,t2=5.0 s
ω2=6(5.0)3+2(5.0)2→ω2=800 rad s-1
No comments:
Post a Comment