flywheel, a  solid disk with moment of inertia 2.5 kg-m2, spins on a central axis at 400 RPM.  A brake is applied, resulting in a constant slowing torque of 15 Nm.  How many revolutions does the wheel make before it stops

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A flywheel, a  solid disk with moment of inertia 2.5 kg-m2, spins on a central axis at 400 RPM.  A brake is applied, resulting in a constant slowing torque of 15 Nm.  How many revolutions does the wheel make before it stops?

**Problem Statement:**

A flywheel, a solid disk with a moment of inertia of 2.5 kg-m², spins on a central axis at 400 RPM. A brake is applied, resulting in a constant slowing torque of 15 Nm. How many revolutions does the wheel make before it stops?

**Explanation:**

- **Flywheel**: A rotating mechanical device that stores rotational energy.
- **Moment of Inertia (I)**: A measure of an object's resistance to changes in its rotation, given as 2.5 kg-m².
- **Initial Angular Velocity**: The flywheel spins at 400 revolutions per minute (RPM).
- **Torque (τ)**: A force that causes rotation, applied as a constant slowing torque of 15 Nm.

This problem explores concepts in rotational dynamics, including angular deceleration due to applied torque and the calculation of total revolutions until a complete stop.
Transcribed Image Text:**Problem Statement:** A flywheel, a solid disk with a moment of inertia of 2.5 kg-m², spins on a central axis at 400 RPM. A brake is applied, resulting in a constant slowing torque of 15 Nm. How many revolutions does the wheel make before it stops? **Explanation:** - **Flywheel**: A rotating mechanical device that stores rotational energy. - **Moment of Inertia (I)**: A measure of an object's resistance to changes in its rotation, given as 2.5 kg-m². - **Initial Angular Velocity**: The flywheel spins at 400 revolutions per minute (RPM). - **Torque (τ)**: A force that causes rotation, applied as a constant slowing torque of 15 Nm. This problem explores concepts in rotational dynamics, including angular deceleration due to applied torque and the calculation of total revolutions until a complete stop.
Expert Solution
Step 1

Moment of inertia of solid disk=(1/2)MR2

Torque=Iα

I=moment of inertia

α=angular acceleration

According to rotational kinematics

ω2-ω02=2αθ

ω=final angular velocity

ω0=Initial angular velocity

θ=no. of revolutions=Angular displacement

 

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