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 by

ENERGY AND MOMENTUM: Translational and Rotational Kinetic Energy

When determining the final kinetic energy ( KE ) of falling objects, we need not ( in theory ) concern ourselves with anything other than the linear pathway traveled to the earth’s surface. To the contrary, an object that rolls top to bottom down an incline will gain both linear ( KE ) and rotational

ROTATIONAL MOTION: At What Rate will the Yo-Yo Accelerate?

Several forces must be taken into account to study the motion of a yo-yo. If we assume a hand to be stationary when a yo-yo begins its descent, a tension force acts upward upon the yo-yo’s string. Opposite to the tension force is the force exerted upon the system by the gravitational force of attraction

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.

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 of

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 angular

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 a

CENTRIPETAL ACCELERATION

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 solution

ENERGY AND MOMENTUM: Which Object Will Roll Down a Hill More Rapidly?

If a buggy and a sphere of equal masses begin rolling side-by-side down a hill, which will reach the bottom of the hill first ( neglecting wind resistance ) ? For simplicity, we should pretend that the energy transfer in this problem is 100% efficient: no losses occur due to sound, random vibrations, or wind

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 same