You have a rotating turntable affixed radially with four protruding pencils. The pencils were found to trip the photogate 32 times per second. Two light objects A and B are taped on top of the turntable at distances 4 cm and 12 cm respectively from the center. What are the tangential velocities of A and B
The tangential velocity of an object rotating on a turntable can be calculated using the formula:
v = 2πr/T
where v is the tangential velocity, π is approximately equal to 3.14, r is the distance from the center of rotation to the object, and T is the time taken for one complete rotation (in this case, the time taken for the photogate to be tripped 32 times, which is 1/32 seconds).
For object A, which is taped at a distance of 4 cm (0.04 m) from the center:
v_A = 2π × 0.04 / (1/32)
v_A = 8π m/s
For object B, which is taped at a distance of 12 cm (0.12 m) from the center:
v_B = 2π × 0.12 / (1/32)
v_B = 24π m/s
Therefore, the tangential velocity of object A is 8π m/s and the tangential velocity of object B is 24π m/s.