A wheel initially has an angular velocity of 18 rad/s, but it is slowing at a constant rate of 2 rad/s 2. By the time it stops, it will have turned through approximately how many revolutions?

1. 65

2. 39

3. 52

4. 26

5. 13

5) 13 revolutions (approximately)

Explanation:

We apply the equations of circular motion uniformly accelerated:

ωf² = ω₀² + 2α*θ Formula (1)

Where:

θ : angle that the body has rotated in a given time interval (rad)

α : angular acceleration (rad/s²)

ω₀ : initial angular speed (rad/s)

ωf : final angular speed (rad/s)

dа ta:

ω₀ = 18 rad/s

ωf = 0

α = - 2 rad/s²; (-) indicates that the wheel is slowing

Revolutions calculation that turns the wheel until it stops

We apply the formula (1)

ωf² = ω₀² + 2α*θ

0 = (18) ² + 2 (-2) * θ

4*θ = (18) ²

θ = (18) ²/4 = 81 rad

1 revolution = 2π rad

θ = 81 rad * 1 revolution / 2πrad

θ = 13 revolutions approximately