Hi! I am going to apply for a medical study admission test and where just wondering if you guys could help me to come up with the formula for solving this problem. I am not looking for a answer, just the mathematical formula to solve theese kind of questions.
The question is as follows:
An object is moving uniformly in circles with a radius of 5m and a frequency of 2 Hz. What is its instantaneous velocity?
2Hz = 2 cycles/s(c/s).
Circumference = pi*2r = 3.14 * 10 = 31.4 m.
V = 2c/s * 6.28rad/c = 12.56 rad/s
Sure! To find the instantaneous velocity of an object moving in uniform circular motion, you can use the formula:
Instantaneous velocity = 2πrf
Where:
- π (pi) is a mathematical constant approximately equal to 3.14
- r is the radius of the circle
- f is the frequency of the motion
In your case, the radius of the circle is given as 5m and the frequency is given as 2 Hz. Thus, the formula can be applied as follows:
Instantaneous velocity = 2π * 5m * 2 Hz
You can simplify this by evaluating 2π, which is approximately 6.28, and then multiplying it by 5m and 2 Hz:
Instantaneous velocity = 6.28 * 5m * 2 Hz
Now, you can perform the calculation:
Instantaneous velocity = 62.8 m/s
Therefore, the instantaneous velocity of the object is approximately 62.8 m/s.
Please note that this formula assumes that the object is moving in uniform circular motion and does not consider any other forces acting on it.