An electrical motor spins at a constant 2695.0 rpm. If the armature radius is 7.165 cm, what is the acceleration of the edge of the rotor?

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BlackTom AI · Accepted Answer

Question restatement: An electrical motor spins at a constant 2695.0 rpm. If the armature radius is 7.165 cm, what is the acceleration of the edge of the rotor?

Options to evaluate: 572 400 m/s2, 281.6 m/s2, 5707 m/s2, 28.20 m/s2

Step 1: Convert rotational speed to angular velocity. 
- The spin rate is 2695 revolutions per minute (rpm).
- Convert to revolutions per second: 2695 / 60 ≈ 44.9167 rev/s.
- Angular velocity ω = 2π × (revolutions per second) ≈ 2π × 44.9167 ≈ 282.6 rad/s.

Step 2: Convert radius to meters. 
- The edge radius is 7.165 cm, which equals 0.07165 m.

Step 3: Use the centripetal (edge) acceleration formula for circular motion: a = r × ω^2.
- Compute ω^2: (282.6 rad/s)^2 ≈ 79800 (rad^2/s^2).
- Multiply by radius: a ≈ 0.07165 m × 79800 s^-2 ≈ 5710 m/s^2.

Now evaluate each option against the calculated magnitude:

- Option: 572 400 m/s^2
  This value is roughly 100 times larger than the calculation. The discrepancy suggests an error in placing decimal points or in using a radius an order of magnitude too large. It is not consistent with a ≈ 5.7×10^3 m/s^2 result.

- Option: 281.6 m/s^2
  This is about a factor of 20 smaller than the computed value. Since a = rω^2 with r > 0 and ω > 0, halving ω or drastically reducing r would be required to reach this magnitude, which does not align with the given data.

- Option: 5707 m/s^2
  This is very close to the calculated value of approximately 5710 m/s^2. The number matches the order of magnitude and the dependence on r and ω that come from a = rω^2, given the provided rpm and radius.

- Option: 28.20 m/s^2
  This is an order of magnitude smaller than the expected result. It could be produced if either the radius were tiny or the angular velocity were drastically reduced, neither of which is consistent with the provided RPM and radius.

Synthesis: The correct approach uses a = rω^2 with r = 0.07165 m and ω ≈ 282.6 rad/s, yielding a value around 5.7×10^3 m/s^2. The remaining options deviate by large factors due to miscalculation of ω, incorrect radius units, or misplaced decimal points.

Note on unit consistency and typical pitfalls: ensure the radius is in meters when applying a = rω^2, and convert rpm to rad/s accurately via ω = 2π × (rpm/60). Small mistakes in these conversions quickly lead to large errors in the final acceleration.

SPHY001 Practice Quiz - Unit 06 | LA046

An electrical motor spins at a constant 2695.0 rpm. If the armature radius is 7.165 cm, what is the acceleration of the edge of the rotor?

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