A solid cylinder rotates about a fixed axis passing through the center of the cy

Question

A solid cylinder rotates about a fixed axis passing through the center of the cylinder as shown below with an angular velocity of 6.69 rad/s. The cylinder has a radius r = 1.64 m, a mass m = 10.15 kg, and is 4.73 meters long.

What is the cylinder's kinetic energy? _________Joules

The cylinder's rotation increases to 9.69 rad/s over the course of 58 seconds. Assuming the torque applied to the cylinder to make this change was steady throughout this time frame, what was the magnitude of this torque?

_____________ N*m

A solid cylinder rotates about a fixed axis passing through the center of the cylinder as shown below with an angular velocity of 6.69 rad/s. The cylinder has a radius r = 1.64 m, a mass m = 10.15 kg, and is 4.73 meters long. What is the cylinder's kinetic energy? _________Joules The cylinder's rotation increases to 9.69 rad/s over the course of 58 seconds. Assuming the torque applied to the cylinder to make this change was steady throughout this time frame, what was the magnitude of this torque? _____________ N*m

Explanation / Answer

Here ,

for a cyclinder , I = 0.5 * mr^2

I = 0.5 * 10.15 * 1.64^2

I = 13.65 Kg.m^2

Now , Kinetic energy = 0.5 * I*w^2

Kinetic energy = 0.5 * 13.65 * 6.69^2

Kinetic energy = 305.5 J

the Kinetic energy of the cyclinder is 305.5 J

now,

time t= 58 s

Using first equation of motion

9.69 = 6.69 + a*58

a = 0.0517 m/s^2

Now , Using second law of motion,

Torque = 0.0517 * 13.65

Torque = 0.71 N.m

the torque acting on the cyclinder is 0.71 N.m

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