Final answer:
To calculate the angular distance a wheel travels before coming to rest under constant angular deceleration, use kinematic equations for rotational motion. The wheel with initial angular speed 3 rad/s and angular deceleration of 5 rad/s² will travel 0.9 radians before stopping.
Step-by-step explanation:
The question involves calculating the angular distance a wheel will travel under a constant angular deceleration until it comes to rest. Given the initial angular speed of 3 rad/s and a constant angular deceleration of 5 rad/s², we can use the kinematic equation for rotational motion:
θ = ω₀×t + (1/2)×α×t²,
where θ is the angular distance, ω₀ is the initial angular velocity, α is the angular acceleration (deceleration in this case, so it's negative), and t is the time. To find the time t when the wheel comes to rest, we use the equation:
ω = ω₀ + α×t,
Setting the final angular velocity ω to 0 (since the wheel comes to rest) and solving for t gives:
t = -ω₀ / α,
Plugging the given values (ω₀ = 3 rad/s, α = -5 rad/s²) into this equation, we get t = 3 / 5 = 0.6 s. Substituting t back into the equation for θ gives:
θ = 3×0.6 + (1/2)×(-5)×(0.6)²,
θ = 1.8 - 0.9 = 0.9 rad.
Therefore, the wheel will travel an angular distance of 0.9 radians before coming to rest. The correct option for the angular distance travelled by the wheel is 0.9 rad.