The flywheel is initially at rest. A force of 250 N is applied tangentially to the rim, causing it to rotate about its central axis.
what is the energy acquired by it after 1 minute?
can anyone help me with this?
What is the KE after one minute:
angular acceleration=torque/momentInertia
torque= 250*r
if the flywheel is a solid disk, moment of interia is 1/2 Mass*r^2 (Check that).
angular acceleration= 500/rM
then finally, angular velocity=acceleration*time
wf= 500/rM * 60
and KE= 1/2 I w^2= 1/2 (1/2 Mr^2)(500/rM)^2= and that is it. Check my work and thinking.
To determine the energy acquired by the flywheel after 1 minute, we need to consider the rotational work done on it.
Rotational work is calculated using the formula: Work = Torque x Angle
In this case, the torque can be determined by multiplying the force applied tangentially to the rim by the radius of the flywheel. Let's assume the radius of the flywheel is given as 0.5 meters.
Torque = Force x Radius = 250 N x 0.5 m = 125 Nm
Now, we need to determine the angle through which the flywheel rotates. Since we know the time, we can use the rotational equivalent of speed, which is angular velocity (ω), given by ω = θ/t, where θ is the angle in radians and t is the time taken.
Let's assume the flywheel has completed one full rotation in one minute. One full rotation equals 2π radians.
θ = 2π radians
t = 1 minute = 60 seconds
Now we can calculate the angular velocity:
ω = θ/t = 2π radians / 60 seconds ≈ 0.1047 radians/second
Substituting the values into the rotational work formula:
Work = Torque x Angle = 125 Nm x 2π radians ≈ 785.4 Joules
Therefore, the energy acquired by the flywheel after 1 minute is approximately 785.4 Joules.