Question

A second athlete in a track and field competition accelerates a hammer of 4 kg from rest at 23.4 rad/s/s over 2.4 seconds. If the radius of rotation is 1.6 m, calculate the tangential component of acceleration if the linear velocity of the hammer at release is 25 m/s.

Answer 1

Given that,

Mass = 4 kg

Acceleration = 23.4 rad/s²

Time = 2.4 sec

Radius = 1.6 m

Linear velocity = 25 m/s

We need to calculate the angular acceleration

Using formula of angular acceleration

$\alpha=\dfrac{\Delta \omega}{t}$

Put the value into the formula

$\alpha=\dfrac{23.4-0}{2.4}$

$\alpha=9.75\ rad/s^2$

We need to calculate the tangential component of acceleration

Using formula of tangential acceleration

$a_{t}=r\alpha$

Put the value into the formula

$a_{t}=1.6\times9.75$

$a_{t}=15.6\ m/s^2$

Hence,  The tangential component of acceleration is $15.6\ m/s^2$