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A point located on the second hand of a large clock has a radial acceleration of 0.1 cm/s². How far is the point from the axis of rotation?

a) 0.1 cm
b) 1.0 cm
c) 10.0 cm
d) 100.0 cm

1 Answer

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Final answer:

To find the distance of the point from the axis of rotation, we need to use the formula for radial acceleration and rearrange it to find the distance. Then, we can use the formula for tangential speed, given the angular velocity of the second hand. By substituting the values and solving the equation, we can determine the distance from the axis.

Step-by-step explanation:

To find the distance of the point from the axis of rotation, we can use the formula:

radial acceleration = (tangential speed)^2 / (distance from the axis)

Given that the radial acceleration is 0.1 cm/s², we need to rearrange the formula to solve for the distance from the axis:

distance from the axis = (tangential speed)^2 / radial acceleration

Since we don't have the tangential speed, we need to find it first. We can use the formula:

tangential speed = 2π × (radius) × (angular velocity)

For the second hand of a clock, the angular velocity is 1 revolution per minute, which is equal to 2π radians per minute. Converting to radians per second, we get:

angular velocity = 2π × (1/60) radians per second

Now we can substitute the values into the formula:

tangential speed = 2π × (radius) × (angular velocity)

Finally, substitute the tangential speed value into the distance formula to find the distance from the axis:

distance from the axis = (tangential speed)^2 / radial acceleration

Solving this equation will give us the answer.

User Carlos Perez
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