To solve this problem, we need to use the equations of motion in angular form.

The equation we need is θ = ωi*t + 0.5*α*t^2, where θ is the angular displacement, ωi is the initial angular velocity, α is the angular acceleration, and t is the time.

First, we need to convert the initial angular velocity from revolutions per minute (rpm) to radians per second (rad/s) because the angular acceleration is given in rad/s^2.

1 revolution = 2π radians, and 1 minute = 60 seconds.

So, ωi = 34.5 rpm * (2π rad/1 rev) * (1 min/60 s) = 3.61 rad/s.

Now we can substitute the values into the equation:

θ = ωi*t + 0.5*α*t^2
θ = 3.61 rad/s * 1.52 s + 0.5 * -2.38 rad/s^2 * (1.52 s)^2
θ = 5.49 rad - 2.75 rad = 2.74 rad

Finally, we need to convert the angular displacement from radians to revolutions because the answer choices are given in revolutions.

1 revolution = 2π radians, so θ = 2.74 rad * (1 rev/2π rad) = 0.436 rev.

So, the angular displacement while the block slows to a stop is 0.436 revolutions.

Question

To solve this problem, we need to use the equations of motion in angular form.

The equation we need is θ = ωi*t + 0.5*α*t^2, where θ is the angular displacement, ωi is the initial angular velocity, α is the angular acceleration, and t is the time.

First, we need to convert the initial angular velocity from revolutions per minute (rpm) to radians per second (rad/s) because the angular acceleration is given in rad/s^2.

1 revolution = 2π radians, and 1 minute = 60 seconds.

So, ωi = 34.5 rpm * (2π rad/1 rev) * (1 min/60 s) = 3.61 rad/s.

Now we can substitute the values into the equation:

θ = ωi*t + 0.5*α*t^2
θ = 3.61 rad/s * 1.52 s + 0.5 * -2.38 rad/s^2 * (1.52 s)^2
θ = 5.49 rad - 2.75 rad = 2.74 rad

Finally, we need to convert the angular displacement from radians to revolutions because the answer choices are given in revolutions.

1 revolution = 2π radians, so θ = 2.74 rad * (1 rev/2π rad) = 0.436 rev.

So, the angular displacement while the block slows to a stop is 0.436 revolutions.

Knowee AI · Accepted Answer

To solve this problem, we need to use the equations of motion in angular form.

The equation we need is θ = ωi*t + 0.5*α*t^2, where θ is the angular displacement, ωi is the initial angular velocity, α is the angular acceleration, and t is the time.

First, we need to convert the initial angular velocity from revolutions per minute (rpm) to radians per second (rad/s) because the angular acceleration is given in rad/s^2.

1 revolution = 2π radians, and 1 minute = 60 seconds.

So, ωi = 34.5 rpm * (2π rad/1 rev) * (1 min/60 s) = 3.61 rad/s.

Now we can substitute the values into the equation:

θ = ωi*t + 0.5*α*t^2
θ = 3.61 rad/s * 1.52 s + 0.5 * -2.38 rad/s^2 * (1.52 s)^2
θ = 5.49 rad - 2.75 rad = 2.74 rad

Finally, we need to convert the angular displacement from radians to revolutions because the answer choices are given in revolutions.

1 revolution = 2π radians, so θ = 2.74 rad * (1 rev/2π rad) = 0.436 rev.

So, the angular displacement while the block slows to a stop is 0.436 revolutions.

A 6.93 kg steel block is spun around a motor at 34.5 rpm. The angular acceleration of the block is -2.38 rads/s2 and it takes 1.52 s for the block to come to a complete stop. What is the angular displacement while the block slows to a stop? 0.436 rev 2.74 rev 7.91 rev 49.7 rev

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