Respuesta :
Answer:
A and C
Explanation:
- The cylinder will travel a smaller circumference in the same time, so its speed will decrease; since the circumference has decreased by a factor of 2, the speed will decrease by a factor of 2
- The centripetal acceleration varies with v^2/r. Where v is speed and r is the distance from cylinder and the center of turntable.
- v decreases by a factor of 2, so v^2 decreases by a factor of 4; r decreases by a factor of 2 so v^2/r decreases by a factor of 2;
- Hence, the acceleration decreases
Answer:
Options A & C accurately describe the motion of the cylinder at the new location
Explanation:
First of all, let's find the speed of the cylinder at the new location. If we assume that the cylinder makes one complete turn in a period
of time.
Thus, Speed v = πR/T
Therefore at the new location, since R would now be R/2, v = πR/2T it's clear the the speed has now decreased which corresponds to option A.
Now for the acceleration,
In centripetal motion, the acceleration of an object that moves in a circular path of radius with constant speed has a
magnitude given by ;
a = v²/R
From earlier, we established that both the velocity and radius of the trajectory change whenever the cylinder is moved.
Since v is now πR/2T
thus, replacing v in the acceleration equation to get;
a = (πR/2T)²/R = π²R/4T²
Comparing with the initial acceleration of a = v²/R = π²R/T², it's clear that the acceleration has decreased by a factor of 4. So the magnitude of the acceleration has decreased which corresponds to option C.
