Question

A disc rotating about its axis from rest acquires the angular speed 100 rev/s in 4s. the angle rotated by it during these 4ss quora

Answer 1

The initial angular velocity = 0

Final = 100 rev/s

The angular acceleration is :

a = (100 - 0) /4 = 25 rev/s²

dФ/dt =  ω

ω = angular velocity:

dФ/dt =( 25 rev/s²) t

S = 25(2π)t rad /s = 50πt rad/s

S = angular displacement.

Ф = ₀∫⁴50πt dt = [50/2πt²]₀⁴

= 25π × 4² = 400π

Ф = angle rotated = 400π

Answer 2

Hello, here’s the answer

Given,

f = 100 rev/s

w(omega) = 2pif

w = 2pi(100)

w = 200pi

Now,

a = w(final) - w(initial)/time

a = 200pi - 0/4

a = 50pi

By using position-time relationship,

Theta = w(initial)time + a(time)^2/2

Theta = 0 + 50pi(4)^2/2

Theta = 400pi

Hope it’ll help