Now let\'s consider the tangential and radial components of a discus as it is be

Question

Now let's consider the tangential and radial components of a discus as it is being thrown. A discus thrower turns with angular acceleration ?=50rad/s2, moving the discus in a circle of radius 0.80 m (Figure 1) . Find the radial and tangential components of acceleration of the discus (modeled as a point) and the magnitude of its acceleration at the instant when the angular velocity is 10 rad/s .

SET UP As shown in (Figure 2) , we model the thrower's arm as a rigid body, so r is constant (this may not be completely realistic). We model the discus as a particle moving in a circular path.

SOLVE The components of the acceleration are given by

aradatan==?2r=(10rad/s)2(0.80m)=80m/s2r?=(0.80m)(50rad/s2)=40m/s2

The magnitude of the acceleration vector is

a=arad2+atan2???????????=89m/s2

REFLECT The magnitude of the acceleration is about nine times the acceleration due to gravity; the corresponding force supplied by the thrower's arm must be about nine times the weight of the discus. Note that we have omitted the unit radian in our final results; we can do this because a radian is a dimensionless quantity.

Part A - Practice Problem:

What is the direction of the acceleration vector of the discus if the angular acceleration is 25 rad/s2 and ?=10rad/s?

Express your answer in degrees to two significant figures. Measure the angle from the radial line between the center of the discus and the thrower's shoulder.

Explanation / Answer

tangential acceleration(T)=r*a ; a-angular acceleration

                                     = 0.8*25=20ms-2

centripretal acceleration(C)= w2/r ; w-angular velocity

                                       = 102/0.8 =125 ms-2

Let A be the angle,

tan(A)=T/C = 20/125

A=9.090 =9.10

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