Question

A point on a rotating turntable 17.5 cm from the center accelerates from rest to a final speed of 0.780 m/s in 2.00 s. At t 1.24 s, find the magnitude and direction of each of the following. (a) the radial acceleration 0.134 Your response is off by a multiple of ten. m/s2 toward the center away from the center in the direction of the rotation in a direction opposite to the rotation (b) the tangentia acceleration 0.39 m/s2 toward the center O away from the center in the direction of the rotation in a direction opposite to the rotation (c) the total acceleration of the point m/s2 inward from the path

Answer 1

Step 1 - In order to find the acceleration, we firstly apply first equation of motion and then calculate the acceleration (equation 1)

Step 2- For part a) radial acceleration for a mass = v^{​​​​​​2}​​​​​/r, where r is the radius.

Since, we know t=1.24s and a =0.39 m/s ² from equation 1. We put these values in first equation of motion and find v and hence find radial acceleration.

Step 3- For part b) tangential acceleration is given by = dv/dt.

From first equation of motion, v=u+at , therefore, dv/dt =a = 0.39 m/s ²

Step 4- For part c) netacceleration is √(a_{​​​​​​ radial})² + (a _tangential)²

^{_{​​​​​​}}further elaboration can be seen in the given pictures