Momentum
The total momentum of a system is constant whenever the vector sum of the external forces on the system is zero.
What is conservation of momentum?
K = (1/2)Iw^2
What is the kinetic energy of a rigid body rotating about a stationary axis?
What is the definition of angular momentum?
This type of collision conserves both momentum and kinetic energy.
What is an elastic collision?
A client has come to you with two metal balls of the same size and mass. He thinks that one might be solid and the other might be hollow inside. By rolling both balls down a slope, how could you tell which one is hollow and which is solid?
Roll the balls down an incline—the solid ball will roll faster. The hollow ball has more mass situated far from the center of rotation, so it will have a larger moment of inertia than the solid ball, which has more mass near the center of rotation.
When I am working a static-equilibrium problem, how do I know where to put the axis of rotation?
You can put it anywhere you wish because nothing is actually rotating. The axis is simply needed to calculate the torques, so you want to pick a convenient location.
When an object explodes into two fragments, the lighter one gets more kinetic energy than the heavier one. How can this be so, since both fragments are acted upon by the same force for the same amount of time during the explosion? (Hint: Does the force act over the same distance on each fragment?)
Being Newton third law forces, these forces are exerted over an identical time interval. However, the resulting acceleration of the lighter fragment is greater than that of the heavier fragment, so the lighter fragment travels farther while the force is exerted. As we learned in Chapter 7, this results in greater work W = Fs being done on the lighter fragment, which in turn results in a greater change in kinetic energy. This explains why the lighter fragment gains more kinetic energy than the heavier fragment.
The tires on a new compact car have a diameter of 2.0 ft and are warranted for 60,000 miles. Determine the angle (in radians) through which one of these tires will rotate during the warranty period.
3.2E8 rad
A person exerts a force of 55 N on the end of a door 74 cm wide. What is the magnitude of the torque if the force is exerted (a) perpendicular to the door, and (b) at a 45º angle to the face of the door?
(a) 41 N*m
(b) 29 N*m
A 5.00 g bullet traveling horizontally at 450 m/s is shot through a 1.00 kg wood block suspended on a string 2.00 m long. If the center of mass of the block rises a distance of 0.450 cm, find the speed of the bullet as it emerges from the block.
What is 391 m/s?
A machine part rotates at an angular speed of 0.60 rad/s; its speed is then increased to 2.2 rad/s at an angular acceleration of 0.70 rad/s^2. Find the angle through which the part rotates before reaching this final speed.
3.2 rad
Calculate the angular momentum and kinetic energy of a solid uniform sphere with a radius of 0.105 m and a mass of 11.5 kg if it is rotating at 5.80 rad/s about an axis through its center. (10.21)
angular momentum: 0.484 kg*m^2/s
kinetic energy: 1.45 J
On a frictionless table, a 3.00 kg block moving at 4.00 m/s to the right collides with an 8.00 kg block moving 1.50 m/s to the left. (a) If the two blocks stick together, what is their final velocity? (b) Calculate both final velocities if the above masses were to collide elastically.
(a) 0 m/s
(b) v1f = -4.00 m/s; v2f = 1.5 m/s
A 55 kg woman is riding a 24 kg bike at a speed of 7 m/s. The wheels of the bike can be treated as thin rings, each of mass 3 kg and radius 0.33 m. What is the total kinetic energy of the woman–bike system?
2082.5 J
When a skater’s hands and arms are brought
in and wrapped around his body to execute a spin, the hands and arms can be considered a thin-walled hollow cylinder. His hands and arms have a combined mass of 8.0 kg. When outstretched, they span 1.8 m; when wrapped, they form a cylinder of radius 25 cm. The moment of inertia about the axis of rotation of the remainder of his body is constant and equal to 0.40 kg*m^2. If the skater’s original angular speed is 0.40 rev/s, what is his final angular speed? (10.28)
1.14 rev/s