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A wheelis under a constant angular deceleration of 5rad/s suqer .It's initial speed is 3rad/s . what angular distance will it travel just before coming to rest?

User Ali Akber
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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.

User Belykh
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