Question

A car is moving from rest.after 10 seconds it's wheels rotate 360 times in 1 minute. if the radius of the wheel is 50cm,then find 1.angular acceleration and 2.angular velocity after 30 seconds

Answer 1

Answer:

24π rad/s

Explanation:

A car is moving is moving from rest , it means intial angular speed of wheels , ω₀ = 0

wheels of car rotates 360 times per minute

angular speed after 1 minutes ,

ω = 2πn/T = 2π × 360/60 rad/sec

ω = 2π × 6 = 12π rad/sec

use formula

ω = ω₀+ αt

Here α is angular acceleration

Given, ω = 12π rad/s

ω₀ = 0 rad/s

t = 30 sec

∴ 12π = 0 + α × 30

α = 12π/30 = 2π/5 rad/s²

angular velocity after 30 sec

ω' = ω + αt

= 12π + 2π/5 × 30

=24π rad/s