The torque required for the cylinder is 76.99 N m.
What is torque?
Torque may be defined as the product of the force and the distance perpendicular to the force from the axis of rotation.
Calculation of the angular acceleration:
The first kinematic equation for the rotational motion is,
ω=ω₀+αt
where ω₀ is the initial angular velocity, ω is the final angular velocity, α is the angular acceleration and t is the time. Since the cylinder starts from the rest, its initial angular velocity is zero.
Here, ω=320 rev/min or ω=320*2π/60 rad/sec, ω₀=0 and t=8.00 sec. Put these values in the above equation and solve it to get the value of angular acceleration.
320*2π/60=0+α*8
α=320*2π/(8*60)
α=4.19 rad/s^2
Calculation of the torque:
The torque T is given by the formula,
T=Iα
where I is the moment of inertia.
For the cylinder, I=1/2*mr^2
where m is the mass of the cylinder and r is the radius of the cylinder.
So,
T=1/2*mr^2*α
Here m=75 kg, radius r is half of the diameter r=1.4/2=0.7 m, and α=4.19 rad/s^2. Using these values in the formula of torque.
T=1/2*(75)*(0.7)^2*4.19
T= 76.99 N m
Learn more about the torque.
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