a stone tied to the end of string 80 cm long whirled in a horizontal circle with a constant speed the stone makes 14 revolutions in 25 sec
a)what is the total angle in radian described by the stone in 25 sec
b)find the angular speed of the stone?
c)find the speed of the stone
d) find the direction and magnitude of the acceleration
14 * 2 pi radians or 14 * 360 degrees
b) 28 pi radians/ 25 seconds = Omega
c) v = Omega * R = 28 pi * 0.8 / 25 meters/second
d) I assume you know formulas for centripetal acceleration so I do not have to derive v^2/r
either v^2/R or R omega^2 toward the middle
To solve these problems, we need to use the formulas and equations of circular motion. Let's break it down step by step:
a) To find the total angle in radians described by the stone in 25 seconds, we need to first find the angle per revolution and then multiply it by the total number of revolutions made in 25 seconds.
1 revolution = 2π radians (equivalent to one full circle)
Angle per revolution = 2π radians
Total angle in radians = Angle per revolution * Total number of revolutions
= 2π * 14
Calculate the value to get the final answer.
b) To find the angular speed of the stone, we use the formula:
Angular speed (ω) = Angle / Time
In this case, the Angle is the total angle described by the stone (which we found in part a) and the Time is given as 25 seconds. Substitute the values into the formula and calculate the angular speed.
c) To find the speed of the stone, we use the formula:
Speed (v) = Circumference / Time
The circumference of the circular path is given by the length of the string, which is 80 cm. The time is again given as 25 seconds. Substitute these values into the formula and calculate the speed.
d) To find the direction and magnitude of the acceleration, we use the formula:
Acceleration (a) = (v^2) / r
Here, v is the speed of the stone (which we found in part c) and r is the radius of the circle. In this case, the radius is the length of the string, which is 80 cm. Convert it to meters and substitute the values into the formula to calculate the acceleration. Note that the direction of the acceleration is towards the center of the circle.
By following these steps and using the relevant formulas, you can find the answers to all the questions.