- #1

pratz

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I need help with this problem...Please someone help...I can't do anything in rotational mechanics:(

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- Thread starter pratz
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In summary, the problem involves a motor rotating at 60rpm that comes to rest in 10 revolutions, with its angular velocity decreasing linearly with angular displacement. To find the angular velocity as a function of time, we can use the formula \omega(\theta) = \omega_0 - C\theta, where \omega_0 is the initial angular velocity and C is a constant. By setting the final angular velocity to zero and solving for C, we can then use the time derivative of this function to determine the angular velocity at t=3 sec.

- #1

pratz

- 1

- 0

I need help with this problem...Please someone help...I can't do anything in rotational mechanics:(

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- #2

cepheid

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To get you started, you know the that the angular velocity is a linearly decreasing function of angular displacement, meaning that:

[tex] \omega(\theta) = \omega_0 - C\theta [/tex]

You know what the inital angular velocity, [itex] \omega_0 [/itex] is, because it is given in the problem. You can calculate the constant by noting that the angular velocity equals zero after ten revolutions: [itex] \omega(10 \textfm{rev}) = 0 [/itex]. Remember to convert everything into radians. Now that you have this function [itex] \omega(\theta) [/itex], you can differentiate it with respect to theta. Can you think of a way of relating that to the time derivative of [itex] \omega[/itex]?

Angular velocity is a measure of how quickly an object is rotating around a fixed point. It is typically measured in radians per second or revolutions per minute.

The formula for angular velocity is ω = θ/t, where ω is the angular velocity, θ is the angular displacement, and t is the time taken to complete the rotation.

The angular velocity of a motor rotating at 60rpm is 1 revolution per second, or 2π radians per second.

Since we know that the motor is rotating at a constant rate of 60rpm and we need to calculate the time taken for 10 revolutions, we can use the formula t = θ/ω. Plugging in the values, we get t = 10/1 = 10 seconds.

The angular velocity of a motor can be affected by various factors such as the torque applied, the mass of the rotating object, and any external forces acting on the motor.

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