centripetal acceleration

ROTATIONAL MOTION: The Frequency and Period of a Pendulum

Q: How may we derive an expression for the frequency ( f ) and period ( T ) of a pendulum? How does the motion of a rotating radius ( r ) within a unit circle relate to the centripetal or “ center seeking “ force that maintains a simple-pendulum system? A: We begin byContinue reading “ROTATIONAL MOTION: The Frequency and Period of a Pendulum”

MAGNETISM AND ELECTROMAGNETISM: Elementary Particle Accelerator Design

The perpendicular force ( FB ) acting upon a positively charged particle moving with a constant velocity ( v ) gives rise to interesting and practical real-world applications: As the equation shows, the magnitude of this force is greatest when it travels through a magnetic field ( B ) at a 90o angle. As aContinue reading “MAGNETISM AND ELECTROMAGNETISM: Elementary Particle Accelerator Design”

ROTATIONAL MOTION: What Distance Separates Two Projectiles Revolving Around a Common Center of Mass?

Q: Two projectiles separated by distance ( dt ) revolve around their center of mass ( cm = ½ dt ). Each projectile has a mass ( m ) of 4.81 x 1020 kg, and they have an instantaneous rotational speed ( ⍵ ) of 1.25 x 10-10 rad/s relative to the center of mass.Continue reading “ROTATIONAL MOTION: What Distance Separates Two Projectiles Revolving Around a Common Center of Mass?”

FORCE AND ACCELERATION: Relative Velocity of Satellites in Orbit

Q: A satellite circles a planet with a tangential velocity of 1.70 x 104 m/s. The orbital radius ( r1 ) is 5.25 x 106 m. A second satellite of equal mass revolves around the same planet with an orbital radius ( r2 ) of 8.60 x 106 m. What is the orbital speed ofContinue reading “FORCE AND ACCELERATION: Relative Velocity of Satellites in Orbit”

ROTATIONAL MOTION: Rotational Inertia

Q: A student sits atop a freely rotating stool holding two dumbbells, each of which has a mass of 3.09 kg. When the student’s arms are extended horizontally outward, the dumbbells are 0.99 m from the axis of rotation. There are 180 degrees of separation between the extended arms. The student rotates with an angularContinue reading “ROTATIONAL MOTION: Rotational Inertia”

CENTRIPETAL FORCE

Q: A 2 kilogram ball is attached to a string that is 10 meters in length. If the tension in the string exceeds 50 Newtons, it will snap. If the ball is swung into rotational motion, what is the maximum speed it can attain and remain intact? A: The tension in the string exerts aContinue reading “CENTRIPETAL FORCE”

Q: What is the centripetal acceleration of a point located 7.50 cm from the central axis of an ultracentrifuge spinning at a rate of 7.5 x 104 rev/min? A: The given rate of 7.5 x 104 revolutions per minute is converted to radians per second ( ⍵ ) in the latter stages of the solutionContinue reading “CENTRIPETAL ACCELERATION”

OSCILLATIONS AND WAVES: The Period of a Pendulum

Q: A pendulum has a length of 2.45 m. How many seconds will it take the pendulum to swing through one complete cycle? Does the mass of the pendulum influence the period? Why or why not? A: This question regards the period ( T ) of a pendulum. The period ( T ) is definedContinue reading “OSCILLATIONS AND WAVES: The Period of a Pendulum”

ENERGY AND MOMENTUM: Artificial Gravity in a Spinning Spacecraft.

Q: A team of engineers is building a spaceship to go to Jupiter. Their design includes a gravity ring, a spinning section where (in the ring’s reference frame) astronauts are pushed outwards by the centrifugal force. In their current design, the ring has to spin once every ten seconds in order to provide the sameContinue reading “ENERGY AND MOMENTUM: Artificial Gravity in a Spinning Spacecraft.”