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5 November, 23:19

What are the average velocity and average acceleration of the tip of a 2.4 cm long hour hand of a clock?

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  1. 5 November, 23:39
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    A circle has a revolution of 360°. Since there are 12 hour markings, each hour interval has an angle of 30°. In radians, that would be equal to π/6 radians. So, in every 1 hour that passes, it covers π/6 of an angle. So, the angular velocity denoted as ω is π/6 : 1 hour = π/6 rad/h. We can compute the average linear velocity, v, from the relationship:

    v = rω, where r is the radius of the circle which is the length of the hour hand

    v = (2.4 cm) (π/6 rad/h)

    v = 1.257 cm/hour

    Therefore, the average velocity is 1.257 cm per hour.

    For the average acceleration, it is equal to zero. The hands of the clock move at a constant velocity. Since acceleration is the change of velocity per unit time, there is no change of velocity because it's constant. That's why it is zero.
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