Question

A car is moving with velocity of 54 km/hr comes to the rest after completing 20
rotations. If the radius of the wheel is 50 cm then find (a) angular acceleration
(b) linear distance travelled by the car before coming to the rest.​

Answer 1

initial angular velocity, $\omega_0$ = v/r

where, v is velocity of car and r is the radius of circular path.

here, v = 54km/h = 54 × 5/18 = 15m/s

and r = 50cm = 0.5m

now, $\omega_0$ = 15/0.5 = 30 rad/s

final angular velocity, ω = 0

angular displacement, θ = 20 rotation = 20 × 2π = 40π radian

using formula, $\omega^2=\omega_0^2+2\alpha\theta$

⇒0 = (30)² + 2α(40π)

⇒-900 = 80α

⇒α = -90/8 = -11.25 rad/s² [Ans]

now linear distance = 20 × 2πr

= 40 × 3.14 × 0.5m

= 20 × 3.14

= 62.8 m

Answer 2

$\huge\bold\purple{Answer:-}$

⇒α = -90/8 = -11.25 rad/s² [Ans]

now linear distance = 20 × 2πr

= 40 × 3.14 × 0.5m

= 20 × 3.14

= 62.8 m