During a tennis serve, a racket is given an angular acceleration of magnitude 170 rad/s2. At the top of the serve, the racket has an angular speed of 18.0 rad/s. If the distance between the top of the racket and the shoulder is 1.10 m, find the magnitude of the total acceleration of the top of the racket.

The magnitude of total acceleration of the top of the racket is 402.5 m/s².

Explanation:

Given:

Angular acceleration of racket (α) = 170 rad/s²

Angular speed of the racket (ω) = 18.0 rad/s

Distance between the top of racket and shoulder (r) = 1.10 m

Now, the magnitude of total acceleration is given as the square root of the sum of the squares of its radial and tangential components.

Radial component of acceleration is given as:

Tangential component of acceleration is given as:

Now, magnitude of total acceleration is given as:

Therefore, the magnitude of total acceleration of the top of the racket is 402.5 m/s².

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