A small object with mass 0.200 kg moves with constant speed in a vertical circle

Question

A small object with mass 0.200 kg moves with constant speed in a vertical circle of radius 0.500 m. It takes the object 0.250 s to complete one revolution

a. What is the translational speed of the object?

(b) What is the frequency?        

(c) As the object passes through the lowest point in its motion, what is the direction of the acceleration of the object? (upward, downward, or acceleration is zero and has no direction.

(d)As the object passes through the lowest point of its motion, what is the magnitude of the acceleration of the object?  

      
part 2. A small object moves at constant speed in a horizontal circle of radius 0.630 m. If the object makes two complete revolutions in one second, what is the magnitude of the acceleration of the object?

part 3. A small object with mass 0.200 kg swings back and forth on the lower end of a light rope that is 3.00 m long. The upper end of the rope is attached to the ceiling. As the object swings through its lowest position, where the rope is vertical, the speed of the object is 5.40 m/s. At this point in the motion, what is the tension in the rope? (Use 9=9.80 m/s^2)

Explanation / Answer

Given that,

mass of the object = m = 0.2 kg ; time taken = t = 0.25 s ; radius = r = 0.5m

(a)translational speed = translational distance/time

translational distance = d = circumference of the circle = 2 pi r

d = 2 x 3.14 x 0.5 = 3.14 m

v = 3.14/0.25 = 12.56 m/s

Hence, the translational speed = v = 12.56 m/s

(b)Frequency is simply 1/t.

f = 1/0.25 = 4 Hz

Hence, frequency = f = 4 Hz

(c)The direction of acceleration would be upwards, as again it has to complete the circle to continue the motion.

(d)We know that, F = ma

as the object is moving in circular path so, it must be experiencing the centripital force F = m v2 / r.

m a = m v2 /r => a = v2 /r = (12.56)2 / 0.5 = 315.51 m/s2.

Hence, the acceleration of the object = 315.51 m/s2.

(PS: humbly requesting you to put the other questions seperately... thanks)

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