The student starts from rest at the center and runs away wit

The student starts from rest at the center and runs away with a constant radial acceleration 0.5 m/s^2(with respect to the platform) as shown. The platform rotates at constant angular velocity 0.2 rad/s. Determine the magnitudes of the student\'s velocity and acceleration after 3 seconds.

Solution

Since Radial acceleration

a_r=V²/R

=>V=sqrt[a_rR]

since Tangential speed

V=RW

=>sqrt[a_rR] =RW

R²W² =a_rR

=>R=a_r/W² =0.5/0.2²

R=12.5 m

So student velocity ater 3 seconds is

V=RW=12.5*0.2

V=2.5 m/s

From

angular acceleration

alpha=W/t =0.2/3 =0.06667 rad/s²

so tangential acceleration is

a_t=R*alpha =12.5*0.06667 =0.8333 m/s²

so net acceleration after 3 seconds

a=sqrt[0.8333²+0.5²]

a=0.972 m/s²