a flywheel of mass 200 kg is rotating at the rate of 8 rps . find the constant torque required to stop the disc in 11 rotations.
during the stop the average speed is 8/2 = 4 rps
11 r/4 r/s = 2.75 seconds to stop
initial angular speed = 2 pi * 8 = 16pi = 50.3 radians/second = Vi
v = Vi + a * t
0 = 50.3 + a * 2.75
a = - 18.3 radians/s^2
Torque = I a = I*= -18.3
I do not know the mass distribution of your flywheel so all I can say is
= something*200 R^2 * -18.3
Why did u take average speed?
To find the constant torque required to stop the flywheel, we need to calculate the initial kinetic energy of the flywheel and the work done to bring it to a stop.
Step 1: Calculate the initial kinetic energy (KE) of the flywheel.
The formula for the kinetic energy of a rotating object is: KE = 1/2 * I * w^2
Where:
- KE is the kinetic energy,
- I is the moment of inertia of the flywheel, and
- w is the angular velocity of the flywheel.
Given:
- Mass of the flywheel (m) = 200 kg
- Angular velocity (w) = 8 rps (revolutions per second)
We need to convert rps to rad/s, as radian measures rotation. Since 1 revolution = 2π radians:
w = 8 rps * 2π rad/1 rev = 16π rad/s
Now, we need to calculate the moment of inertia (I) of the flywheel. The moment of inertia of a disc is given by: I = 1/2 * m * r^2
Where:
- I is the moment of inertia,
- m is the mass of the flywheel, and
- r is the radius of the flywheel.
Given:
- Mass of the flywheel (m) = 200 kg
We need the radius (r) of the flywheel to calculate the moment of inertia. Unfortunately, the radius of the flywheel is not provided in the question. We need this information to proceed with the calculation.