Question

A material point moves in a circular path with a radius of 20 centimeters and performs uniform circular motion with a frequency of 5Hz. Determine the following:

a. What is the linear velocity of the material point?
b. Find the centripetal acceleration of complete rotations performed in 20 seconds.
A) 10 m/s, 100 m/s²
B) 31.4 cm/s, 314 cm/s²
C) 62.8 cm/s, 628 cm/s²
D) 100 m/s, 10 m/s²

Answer 1

The linear velocity of the material point is approximately 628 cm/s and the centripetal acceleration for complete rotations performed in 20 seconds is also approximately 628 cm/s².

Step-by-step explanation:

The linear velocity of a material point moving in a circular path can be calculated using the formula v = 2πrf, where v is the linear velocity, r is the radius of the path, and f is the frequency. In this case, the radius is given as 20 cm and the frequency is 5 Hz, so the linear velocity is:

v = 2π(20 cm)(5 Hz) = 200π cm/s ≈ 628 cm/s

The centripetal acceleration for a complete rotation can be calculated using the formula a = 4π²rf², where a is the centripetal acceleration. In this case, the radius is still 20 cm and the time for a complete rotation is 20 seconds, so the centripetal acceleration is:

a = 4π²(20 cm)(20 cm)/(20 s)² ≈ 628 cm/s²