difference between centripetal acc. and angular acc
no copy paste please explain properly
Answers
Explanation:
Uniform Circular Motion and Gravitation discussed only uniform circular motion, which is motion in a circle at constant speed and, hence, constant angular velocity. Recall that angular velocity ω was defined as the time rate of change of angle θ:
ω
=
Δ
θ
Δ
t
where θ is the angle of rotation as seen in Figure 1. The relationship between angular velocity ω and linear velocity v was also defined in Rotation Angle and Angular Velocity as
v = rω
or
ω
=
v
r
where r is the radius of curvature, also seen in Figure 1. According to the sign convention, the counter clockwise direction is considered as positive direction and clockwise direction as negative
The given figure shows counterclockwise circular motion with a horizontal line, depicting radius r, drawn from the center of the circle to the right side on its circumference and another line is drawn in such a manner that it makes an acute angle delta theta with the horizontal line. Tangential velocity vectors are indicated at the end of the two lines. At the bottom right side of the figure, the formula for angular velocity is given as v upon r.
Figure 1. This figure shows uniform circular motion and some of its defined quantities.
Angular velocity is not constant when a skater pulls in her arms, when a child starts up a merry-go-round from rest, or when a computer’s hard disk slows to a halt when switched off. In all these cases, there is an angular acceleration, in which ω changes. The faster the change occurs, the greater the angular acceleration. Angular acceleration α is defined as the rate of change of angular velocity. In equation form, angular acceleration is expressed as follows:
α
=
Δ
ω
Δ
t
,
where Δω is the change in angular velocity and Δt is the change in time. The units of angular acceleration are (rad/s)/s, or rad/s2. If ω increases, then α is positive. If ω decreases, then α is negative.
EXAMPLE 1. CALCULATING THE ANGULAR ACCELERATION AND DECELERATION OF A BIKE WHEEL
Suppose a teenager puts her bicycle on its back and starts the rear wheel spinning from rest to a final angular velocity of 250 rpm in 5.00 s. (a) Calculate the angular acceleration in rad/s2. (b) If she now slams on the brakes, causing an angular acceleration of -87.3 rad/s2, how long does it take the wheel to stop?
Strategy for (a)
The angular acceleration can be found directly from its definition in
α
=
Δ
ω
Δ
t
because the final angular velocity and time are given. We see that Δω is 250 rpm and Δt is 5.00 s.
Solution for (a)
Entering known information into the definition of angular acceleration, we get
α
=
Δ
ω
Δ
t
=
250 rpm
5.00 s
.
Because Δω is in revolutions per minute (rpm) and we want the standard units of rad/s2 for angular acceleration, we need to convert Δω from rpm to rad/s:
Δ
ω
=
250
rev
min
⋅
2
π
rad
rev
⋅
1
min
60
sec
=
26.2
rad
s
Entering this quantity into the expression for α, we get
α
=
Δ
ω
Δ
t
=
26.2 rad/s
5.00 s
=
5.24
rad/s
2
Explanation:
centripetal acceleration is the acceleration acting towards centre of circular path travelled by an object
angular acceleration is the angular velocity that a spinning body undergoes in a given time interval