The angle turned by a body undergoing circular motion depends on time as θ = θo + θ1t + θ2 t2 . Then the angular acceleration of the body is :

Question

The angle turned by a body undergoing circular motion depends on time as θ = θo + θ1t + θ2 t2 . Then the angular acceleration of the body is : (A) θ1 (B) θ2 (C) 2 θ1 (D) 2 θ2

Tardigrade Admin · Accepted Answer

Angle turned by the body θ=θ0+θ1 t+θ2 t2 =(d θ/d t) =(d/d t)(θ0+θ1 t+θ2 t2) Angular velocity =θ1+2 θ2 t Angular acceleration α =(d ω/d t) =(d/d t)(θ1+2 θ2 t) =2 θ2

Q. The angle turned by a body undergoing circular motion depends on time as $θ = θ_{o} + θ_{1} t + θ_{2} t^{2}$ . Then the angular acceleration of the body is :

$θ_{1}$

$θ_{2}$

$2 θ_{1}$

$2 θ_{2}$

Angle turned by the body
$θ = θ_{0} + θ_{1} t + θ_{2} t^{2}$
$= \frac{d θ}{d t}$
$= \frac{d}{d t} (θ_{0} + θ_{1} t + θ_{2} t^{2})$
Angular velocity $= θ_{1} + 2 θ_{2} t$
Angular acceleration $α = \frac{d ω}{d t}$
$= \frac{d}{d t} (θ_{1} + 2 θ_{2} t)$
$= 2 θ_{2}$

Q. The angle turned by a body undergoing circular motion depends on time as θ=θo​+θ1​t+θ2​t2 . Then the angular acceleration of the body is :

θ1​

θ2​

2θ1​

2θ2​