Question

a car is moving from rest. after 10 seconds its wheels rotate 360 times in a minute. if the radius of the wheel is 50 CM. then find 1) angular acceleration and 2) angular velocity after 30 seconds

Answer 1

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
means angular speed after 1 minutes , ω = 2πn/T = 2π × 360/60 rad/sec
ω = 2π × 6 = 12π rad/sec

Now, use formula
ω = ω₀+ αt
Here α is angular acceleration
Given, ω = 12π rad/s , ω₀ = 0 rad/s and 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