5kg particle is attaced at arim of arotating wheel of radius 2m. the wheel completes each revolution in 3seconds. The total moment of inertia of the sysem(I particle+I wheel) is 2kg.msquare)
find A, Determine the rotational kinetic energy of the system?
B, the work need to stop the rotation?
C,how much torque is required to stop the rotation of the system in 1.2 second?
To determine the rotational kinetic energy of the system, we need to calculate the individual kinetic energies of the particle and the wheel and then add them together.
A) Rotational kinetic energy of the particle:
The formula for rotational kinetic energy is KE = (1/2) * I * ω^2, where KE is the kinetic energy, I is the moment of inertia, and ω is the angular velocity.
For the particle, the moment of inertia is given as 5 kg.m^2, and since it is rotating along the radius of the wheel, its angular velocity (ω) will be the same as the angular velocity of the wheel.
To find the angular velocity (ω) of the wheel, we can use the formula ω = 2π / T, where T is the period of rotation. Here, the period is given as 3 seconds, so ω = 2π / 3 rad/s.
Substituting the values into the formula, the rotational kinetic energy of the particle is KE_particle = (1/2) * 5 kg.m^2 * (2π / 3 rad/s)^2.
B) Rotational kinetic energy of the wheel:
The moment of inertia for the wheel is given as I_wheel = 2 kg.m^2, and its angular velocity is ω_wheel = 2π / 3 rad/s (as calculated above).
The rotational kinetic energy of the wheel is KE_wheel = (1/2) * 2 kg.m^2 * (2π / 3 rad/s)^2.
C) Work needed to stop the rotation:
The work needed to stop the rotation is equal to the total rotational kinetic energy of the system. Therefore, we add the kinetic energies of the particle and wheel together:
KE_total = KE_particle + KE_wheel.
Substituting the values we have calculated, we can find the total rotational kinetic energy.
To find the work done in stopping the rotation, we need to subtract the final rotational kinetic energy (after stopping) from the initial rotational kinetic energy.
C) Torque required to stop the rotation in 1.2 seconds:
To find the torque required to stop the rotation, we can use the formula τ = I * α, where τ is the torque, I is the moment of inertia, and α is the angular acceleration.
First, we need to find the angular acceleration (α) using the formula α = ωf - ωi / t, where ωf is the final angular velocity (0 rad/s when stopped), ωi is the initial angular velocity, and t is the time taken to stop (1.2 seconds).
Substituting the values into the formula, we can find the angular acceleration (α). Finally, we can calculate the torque required to stop the rotation using τ = I * α, where I is the total moment of inertia of the system.