A flywheel comprises a uniform circular disk with a moment of inertia of 64.13 Kg m2. It rotates with an angular velocity of 1106. rpm. A constant tangential force is applied at a radial distance of 0.400 m. What energy (in Kilo Joule) must this force dissipate to stop the wheel?

cant figure out how to do it with out acceleration or time

To find the energy dissipated by the constant tangential force to stop the flywheel, you don't need acceleration or time directly. You can use the concept of work and energy.

Here's the step-by-step process to find the energy dissipated:

Step 1: Convert the angular velocity from rpm to radians per second. Recall that there are 2π radians in one revolution, and 60 seconds in one minute.
Angular velocity (ω) in radians per second = (1106 rpm) × (2π rad/1 rev) × (1 min/60 s) = 115.89 rad/s

Step 2: Use the formula for kinetic energy of rotational motion:
Kinetic energy (KE) = (1/2) × moment of inertia × (angular velocity)^2
KE = (1/2) × (64.13 kg m^2) × (115.89 rad/s)^2

Step 3: Calculate the energy dissipated by the tangential force applied at a radial distance of 0.400 m. The force is responsible for slowing down the flywheel's rotation. For a constant tangential force, the work done is equal to the force multiplied by the distance covered.
Work (W) = force × distance
Work = tangential force × 2π × radial distance

Step 4: Transform the work into energy:
Energy dissipated = Work done

Note: The units of energy in the given question are in Kilo Joules (kJ). Ensure all other quantities are in consistent units to get the answer in kJ.

By following these steps, you should be able to calculate the energy (in kJ) that the force must dissipate to stop the wheel.