A golfer’s hands move through an arc length of 10 cm during a putt. What arc length does the head of the putter move through if the hands are 50 cm from the axis of the rotation and the putter head is 150 cm from the axis of rotation?
Three times as far.
To find the arc length that the head of the putter moves through, we can use the concept of angular velocity.
Angular velocity is defined as the rate of change of angle with respect to time. In this case, the angle is the angle of rotation of the putter head about the axis of rotation.
Let's call the angle of rotation of the putter head θ. The arc length that the hands move through (10 cm) can be related to the arc length that the putter head moves through (let's call it s) using the ratio of their distances from the axis of rotation.
The ratio of the distances from the axis of rotation is given as:
(ratio) = (distance of putter head from axis) / (distance of hands from axis)
(ratio) = 150 cm / 50 cm
(ratio) = 3
In other words, the distance that the putter head moves through is 3 times the distance that the hands move through.
So, we can write the relationship between s (arc length of putter head) and 10 cm (arc length of hands) as:
s = (ratio) * 10 cm
s = 3 * 10 cm
s = 30 cm
Therefore, the arc length that the head of the putter moves through is 30 cm.