An Olympic hammer thrower swings a mass of 7.26 kg at the end of a light inextensible wire in a circular motion - Leaving Cert Physics - Question 12 - 2012
Question 12
An Olympic hammer thrower swings a mass of 7.26 kg at the end of a light inextensible wire in a circular motion. In the final complete swing, the hammer moves at a c... show full transcript
Worked Solution & Example Answer:An Olympic hammer thrower swings a mass of 7.26 kg at the end of a light inextensible wire in a circular motion - Leaving Cert Physics - Question 12 - 2012
Step 1
What is the angular velocity of the hammer during its final swing?
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Answer
To calculate the angular velocity \( \omega \), we use the formula:
\\omega = \frac{2\pi}{T} \\\
where, T is the time taken to complete one full circle. Given that it takes 0.8 seconds:
ω=0.82π≈7.85 rad/s
Step 2
Even though the hammer moves at a constant speed, it accelerates. Explain.
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Answer
Even though the hammer moves at a constant speed, it is undergoing circular motion. This means that the direction of the velocity vector is continuously changing even though its magnitude remains constant. Because acceleration is defined as the rate of change of velocity, and since the direction is changing, there is a centripetal acceleration directed towards the center of the circular path.
Step 3
the acceleration of the hammer during its final swing
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Answer
The centripetal acceleration (
ac) can be calculated using the formula:
a_c = \frac{v^2}{r} \\,$$
Given that the velocity (v) can be calculated from the angular velocity:
