The hour hand on a certain clock is 8.3 cm long.

Find the tangential speed of the tip of this hand.

To find the tangential speed of the tip of the hour hand, you need to know the length of the hour hand and the angular speed at which it rotates.

The length of the hour hand is given as 8.3 cm. This is the radius of the circular path that the tip of the hand travels in.

To calculate the tangential speed, you also need to know the angular speed. The angular speed is the rate at which the angle covered by the hour hand changes over time. In this case, since the hour hand completes one full rotation in 12 hours, the angular speed can be calculated by dividing 360 degrees by the time it takes for one rotation. In this case, since the hour hand completes one full rotation in 12 hours, the angular speed can be calculated by dividing 360 degrees by 12 hours:

Angular speed = 360 degrees / 12 hours = 30 degrees per hour.

Now you have both the radius (8.3 cm) and the angular speed (30 degrees/hour). To find the tangential speed, you can use the formula:

Tangential speed = Radius * Angular speed.

Substituting the values:

Tangential speed = 8.3 cm * (30 degrees/hour).

However, since degrees are not a standard unit, you need to convert degrees to radians. There are 2π radians in 360 degrees, so the angular speed in radians per hour is:

30 degrees / hour * (2π radians / 360 degrees) = π/6 radians per hour.

Finally, substituting the value for the angular speed in radians/hour:

Tangential speed = 8.3 cm * (π/6 radians/hour).

The tangential speed of the tip of the hour hand is approximately 4.32 cm/hour.

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