You have a rotating turntable affixed radially with four protruding pencils. The pencils were found to trip the photogate 32 times per second. The angular velocity is 8pieTwo light objects A and B are taped on top of the turntable at distances 4 cm and 12 cm respectively from the center. With “R” tripled from A to B, what is the fold-change in their “v”
To determine the fold-change in the velocity of objects A and B, we need to consider their respective distances from the center of the turntable.
Let's denote the velocity of object A as v_A and the velocity of object B as v_B.
Given that the angular velocity of the turntable is 8π rad/s, we know that the linear velocity of any point on the turntable is given by the formula v = ω*r, where ω is the angular velocity and r is the distance from the center.
For object A, which is located 4 cm from the center, the distance is r_A = 4 cm = 0.04 m.
Using the formula v = ω*r, we can calculate the velocity of object A:
v_A = (8π rad/s)*(0.04 m) = 0.32π m/s.
For object B, which is located 12 cm from the center, the distance is r_B = 12 cm = 0.12 m.
Using the formula v = ω*r, we can calculate the velocity of object B:
v_B = (8π rad/s)*(0.12 m) = 0.96π m/s.
To determine the fold-change in their velocities, we divide v_B by v_A:
fold-change = v_B / v_A = (0.96π m/s) / (0.32π m/s) = 3.
Therefore, the fold-change in the velocities of objects A and B is 3.