In: Physics
A. A disk of radius 0.15 m spins at a rate of 18 rad/s. What is the linear speed of a point on its outer rim? How long does it take that point to make a complete revolution? What would be given as the frequency in hertz of this motion?
B. A mass and spring system is built with a spring constant of 5.0 N/m and a mass of 2 kg. What is its period of oscillation? What length would a simple pendulum have to have to make an identical mass oscillate with that same period?
A) Given the radius of the disc is R = 0.15m and the angular velocity of the disc is = 18rad/s. So the linear speed on the outer rim is given by,
So the linear speed of the outer rim is 2.7m/s.
The angular displacement in one complete revolution is . So,
So the time taken by the point to make a complete revolution is 0.35s.
The frequency is given by,
So the ferquency of the motion is 2.86Hz.
B) Given the spring constant k = 5N/m and the mass hanging is m = 2kg. So the time period of oscillation is,
So the period of oscillation of spring-mass system is 3.97s.
The time period of a simple pendulum is given by,
So the length of the simple pendulum to make an identical mass oscillate with that same period is 3.91m.