An electric motor is used to accelerate a solid disk (cylinder) flywheel. The flywheel has a mass of 30 kg and a radius of 0.25 m. The flywheel is initially at rest when the elcetric motor applies a torque of 30 Nm for 15 seconds.

What is the final angular speed in revolutions per second of the flywheel?

Round your answer to one (1) decimal place. Do not enter units. Example: 12.3

Question

An electric motor is used to accelerate a solid disk (cylinder) flywheel. The flywheel has a mass of 30 kg and a radius of 0.25 m. The flywheel is initially at rest when the elcetric motor applies a torque of 30 Nm for 15 seconds.

What is the final angular speed in revolutions per second of the flywheel?

Round your answer to one (1) decimal place. Do not enter units. Example: 12.3

BlackTom AI · Accepted Answer

The question involves a solid disk (flywheel) being accelerated by a constant torque. We'll work through the physics step by step.

First, identify the relevant quantities for a solid disk:
- Mass m = 30 kg
- Radius R = 0.25 m
- Moment of inertia I for a solid disk = (1/2) m R^2
Compute I: I = 0.5 × 30 × (0.25)^2 = 15 × 0.0625 = 0.9375 kg·m^2.

Next, use angular impulse–angular momentum relation. A constant torque τ applied for time t gives angular impulse τt, which equals the change in angular momentum Iω: Iω = τt.
Here, the torque τ = 30 N·m and the duration t = 15 s, so the angular impulse is τt = 30 × 15 = 450 N·m·s.

Solve for the final angular speed ω:
ω = (τt) / I = 450 / 0.9375 = 480 rad/s.

Convert rad/s to revolutions per second (rev/s) using the relation 1 rev = 2π rad:
ω (rev/s) = ω / (2π) = 480 / (2π) ≈ 480 / 6.2832 ≈ 76.4 rev/s.

Now about the answer options: the computed value 76.4 matches the listed numeric option shown in the prompt. If you were selecting from multiple choices, this would be the one corresponding to approximately 76.4 rev/s.

Note on potential pitfalls to avoid:
- Forgetting the 0.5 factor in the disk inertia would lead to an incorrect I, and thus a different ω.
- Mixing up units (rad/s vs rev/s) is a common source of error; always convert to the desired unit at the end.
- Using the mass alone without the radius would be insufficient to determine I for a disk; the R^2 term is essential here.

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