Acceleration of a Tennis Racket

[farrah003]

Homework Statement

During a serve, a tennis racket of mass 1.4 kg is given an angular acceleration of 163 rad/sec2. At the top of the serve, the racket has an angular speed of 16 rad/sec.
If the distance between the top of the racket and the shoulder is 1.5 m, what is the total acceleration of the top of the racket?
atotal = m/sec2 ?

Homework Equations

Tangential acceleration = α*r
Centripetal acceleration = ω²*r

The Attempt at a Solution

a = √[at² + ac²]
a = √[(244.5)² + (24)²]
a = 16.3859

 

[PhanthomJay]

Homework Statement

During a serve, a tennis racket of mass 1.4 kg is given an angular acceleration of 163 rad/sec2. At the top of the serve, the racket has an angular speed of 16 rad/sec.
If the distance between the top of the racket and the shoulder is 1.5 m, what is the total acceleration of the top of the racket?
atotal = m/sec2 ?

Homework Equations

Tangential acceleration = α*r
Centripetal acceleration = ω²*r

good.

The Attempt at a Solution

a = √[at² + ac²]

yes!

a = √[(244.5)² + (24)²]
a = 16.3859

In calculating ac, you forgot to square the angular speed, ω.

 

[farrah003]

ohh hahahah thanks !