Question

Angular displacement is said to be of radian when S=r (a) 1 (b) Zero (c) 27 (d) None of these​

Answer 1

Answer:

Explanation:

Chapter 8

Rotational Kinematics:

In Chapter 2, the kinematics of straight line motion was studied where the variables were x, v, a, and t.  In Chapter 2, the cause of motion (force) was not important and force was not used to calculate the acceleration (a) of motion.

In this chapter, the kinematics of rotation will be studied where the variables are θ, ω, α,  and t.   Although these quantities were discussed in Chapter 5, we will review them here again.

Angular Displacement (θ):  

In Fig. 1, angular displacement, θ, pronounced "theta" is the angle swept by radius R of the circle that points to a rotating particle or mass like M.

Angular Velocity (ω):  

Angular velocity, ω, is defined as the change in angular displacement, θ, per unit of time, t.  

Example 1:  An object travels around a circle10.0 full turns in 2.5 seconds.  Calculate (a) its angular displacement, θ, during this period and (b) its average angular speed, ω.

Solution:  (a)    θ = 10.0 turns (6.28 rd/turn) = 62.8 radians.

                (b)   ω  = Δθ/Δt   = 62.8rd / 2.5s  = 25 rd/s.

 

Angular Acceleration (α):  Angular acceleration α is the change in the angular velocity, ω, per unit of time, t.

with the SI unit of rd/s2.  The symbol α is pronounced " Alpha."

Example 2:  A car tire is turning at a rate of 5.0 rd/s as the car travels on a straight road.  The driver accelerates the car uniformly for 6.0 seconds.   As a result, the angular speed of each tire increases to 8.0 rd/s.  Find the angular acceleration of each tire during this period.

Solution: α=Δω/Δt;  α = (ωf - ωi) /Δt ;   α = (8.0rd/s -5.0rd/s)/6.0s  = 0.50 rd/s2.

There is a one to one correspondence between the linear motion formulas and the angular motion formulas that can be similarly derived here.  Table 1 shows this one to one correspondence.  If you know Chapter 2 formulas, it is like you already know Chapter 8 formulas.  The formulas in the middle column relate each angular variable to its counterpart linear

Linear Motion (Chapter 2)

Relations Angular Motion (Chapter 8)

 Variables: x, t, v, and a

 v = Δx /Δt.

 a = Δv /Δt ;  a = ( vf - vi )/Δt.

 x = (1/2) at2  + vi t.

 vf2 - vi2 = 2ax.

x = Rθ  

v = Rω

a = Rα

or

at = Rα*

  Variables:  θ, t, ω, and α

ω = Δθ /Δt.

α  = Δω /Δt  ; α  = (ωf - ωi ) /Δt.

θ = (1/2) α t2 + ωi t.

  ωf2 - ωi2  = 2αθ.

Answer 2

Answer:

(a) 1

Explanation:

for S = r ,

θ = S/r

θ = 1

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