Question

The radius of a car wheel is 0.4 m the car is accelerated from rest by an angular acceleration

Answer 1

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The radius of a wheel of a car is 0.4 m. The car is accelerated from the rest by angular acceleratin of 1.4 radian/sec square for 20 sec. How much diatancethe wheel covers in this time and what will be its linear velocity

Given .  Radius of the wheel  , r = 0.4 m 
     angular acceleration  α   =1.4  rad/ sec2
​             time , t = 20 sec
Initial angular speed of the wheel  wo =0  rad / sec
 Using euquation​
                                θ =w0t +12 αt2θ = 0+ 12 ×1.4 ×20×20      θ=280 radian
Distance covered by the wheel  ​ 
                                       If    ​
                               θ = 2π radian , distance (s) =2π r   ⇒for θ =280 radion , distance (s) = 280 × 0.4 = 112 m linear velocity  , V  =r w      using  w = w0  +α t                    w =1.4×20 = 28 rad/ sec                      V = 0.4×28 = 112 m/s

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