Question

Assume that the motor has accelerated the wheel up to an angular velocity Ï1 with angular acceleration α in time t1. At this point, the motor is turned off and a brake is applied that decelerates the wheel with a constant angular acceleration of â5α. Find t2, the time it will take the wheel to stop after the brake is applied (that is, the time for the wheel to reach zero angular velocity). Express your answer in terms of some or all of the following: Ï1, α, and t1.

Answer 1

t₂ = t₁ / 5

Step-by-step explanation:

Rotational kinematics using: ωf = ωi + αt

Starting from rest and speeding up:

ω₁ = 0 + αt₁ .. Eq1

Starting from ω₁ and slowing to a stop:

0 = ω₁ - 5αt₂

Substituting for ω₁ from Eq 1

0 = αt₁ - 5αt₂

5αt₂ = αt₁

5t₂ = t₁

t₂ = t₁ / 5