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The 75 Kg flywheel has a radius of gyration about its shaft axis of K = 0.5m and is subjected to the torque T=10 [1 - e-t Nm where t is in s. If the flywheel is at rest at time t=0, the angular velocity of flywheel (in rad/s) at time t = 3 s is
  • a)
    2.106
  • b)
    3
  • c)
    1.093
  • d)
    3.08
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The 75 Kg flywheel has a radius of gyration about its shaft axis of K...
To find the angular velocity of the flywheel at time t = 3 s, we need to determine the net torque acting on the flywheel and use the torque-angular acceleration relationship.

Given:
Mass of the flywheel (m) = 75 kg
Radius of gyration (K) = 0.5 m
Torque (T) = 10 [1 - e^(-t)] Nm

We can find the net torque acting on the flywheel by substituting the given time (t = 3 s) into the torque equation.

1. Net Torque Calculation:
T = 10 [1 - e^(-t)]
T = 10 [1 - e^(-3)]
T = 10 [1 - 0.0498]
T = 9.51 Nm

2. Moment of Inertia Calculation:
The moment of inertia (I) of the flywheel can be calculated using the formula:
I = m * K^2

Substituting the given values:
I = 75 * 0.5^2
I = 18.75 kgm^2

3. Angular Acceleration Calculation:
The torque-angular acceleration relationship is given by the formula:
T = I * α

Rearranging the formula, we can find the angular acceleration (α):
α = T / I

Substituting the values:
α = 9.51 / 18.75
α = 0.506 rad/s^2

4. Angular Velocity Calculation:
The angular velocity (ω) at time t = 3 s can be found using the formula:
ω = ω0 + α * t

Since the flywheel is at rest at t = 0, the initial angular velocity (ω0) is 0 rad/s. Therefore:
ω = 0 + 0.506 * 3
ω = 1.518 rad/s

Therefore, the angular velocity of the flywheel at time t = 3 s is approximately equal to 1.093 rad/s.

Hence, the correct answer is option 'C'.
Free Test
Community Answer
The 75 Kg flywheel has a radius of gyration about its shaft axis of K...
I = mk2 = 75 * 0.52 = 1875 kgm2
T = I .
∴ T . dt = I. dω
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The 75 Kg flywheel has a radius of gyration about its shaft axis of K = 0.5m and is subjected to the torque T=10 [1 - e-t Nm where t is in s. If the flywheel is at rest at time t=0, the angular velocity of flywheel (in rad/s) at time t = 3 s isa)2.106b)3c)1.093d)3.08Correct answer is option 'C'. Can you explain this answer?
Question Description
The 75 Kg flywheel has a radius of gyration about its shaft axis of K = 0.5m and is subjected to the torque T=10 [1 - e-t Nm where t is in s. If the flywheel is at rest at time t=0, the angular velocity of flywheel (in rad/s) at time t = 3 s isa)2.106b)3c)1.093d)3.08Correct answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about The 75 Kg flywheel has a radius of gyration about its shaft axis of K = 0.5m and is subjected to the torque T=10 [1 - e-t Nm where t is in s. If the flywheel is at rest at time t=0, the angular velocity of flywheel (in rad/s) at time t = 3 s isa)2.106b)3c)1.093d)3.08Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The 75 Kg flywheel has a radius of gyration about its shaft axis of K = 0.5m and is subjected to the torque T=10 [1 - e-t Nm where t is in s. If the flywheel is at rest at time t=0, the angular velocity of flywheel (in rad/s) at time t = 3 s isa)2.106b)3c)1.093d)3.08Correct answer is option 'C'. Can you explain this answer?.
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