Consider different points along one spoke of a wheel rotating with constant angular velocity. Which of the following is true regarding the centripetal acceleration at a particular instant of time?

a. The magnitude of the centripetal acceleration is greater for points on the spoke closer to the hub than for points closer to the rim
b. both the magnitude and the direction of the centripetal acceleration depend on the location of the point on the spoke.
c. The magnitude of the centripetal acceleration is smaller for points on the spoke closer to the hub than for points closer to the rim but the direction of the acceleration is the same at all points on this spoke.
d. The magnitude and direction of the centripetal acceleration is the same at all points on this spoke.

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Numenius Numenius · Answer 1 · 2021-06-22T02:42:56+02:00

Answer:

Option (a).

Explanation:

Let the angular velocity is w.

The centripetal acceleration is given by

[tex]a = r w^2[/tex]

where, r is the distance between the axle and the spoke.

So, more is the distance more is the centripetal acceleration.

(a) For the points on the spoke closer to the hub than for points closer to the rim is larger distance, so the centripetal force is more.

The statement is true.

(b) The direction of centripetal acceleration is always towards the center, so the statement is false.

(c) It is false.

(d) It is false.

Option (a) is correct.