Rotational momentum

Question 1

Tangential speed

Answer 1

• linear speed of something moving along a circular path
• depends on radial distance (distance from axis)
• directly proportional to the distance form the axis for any given rotational speed
• units = m/s

Question 2

Rotational speed

Answer 2

Angular speed

• number of rotations or revolutions per unit of time
• rotational rates = RPM
• tangential speed is directly proportional to rotational speed at any fixed distance from the axis of rotation

Question 3

Tangential speed ~

Answer 3

Radial distance x rotational speed

Question 4

Tangential acceleration

Answer 4

When tangential speed undergoes a change

• any change in tangential speed indicated an acceleration in the direction of tangential motion
• anything moving in a curved path will also undergo centripetal acceleration

Question 5

Rotational inertia

Answer 5

• an object rotating about an axis tends to remain rotating about the same axis unless interfered with by some external force
• the property of an object to resist changes in its rotational state of motion

Question 6

Rotational inertia (2)

Answer 6

• depends on mass about the axis of rotation
• the great the distance between an object’s mass concentration and the axis, the greater the rotational inertia
• the greater the rotational inertia, the greater the difficulty in changing its rotational state
• the rotational inertia of an object depends on the axis about which it rotates
• the object with the larger rotational inertia relative to its Owen mass has the greater resistance to a change in its motion

Question 7

Torque

Answer 7

Rotational counterpart of force

• force chagnes the motion of things and tends to twist or change the state of rotation of things
• stationary object to move, apply force. Stationary object to rotate, apply torque

Question 8

Torque equation

Answer 8

Torque = lever arm x force

• involves distance form the axis of rotation, which also provide leverage
• net torque on a body or a system must also be zero for mechanical equilibrium

Question 9

Center of mass/gravity

Answer 9

1. COM: the average position of all the mass that makes up the object
2. COG is used to express center of mass. It is the average position of weight distribution

Question 10

COM facts

Answer 10

• the motion of a spinning object is a combination of the straight-line motion of its center of mass and the rotational motion about its COM
• balancing an object provides a simple method of locating its center of gravity
• the center of mass may be a point where no mass exists (ring, boomerang)

Question 11

Stability

Answer 11

• if a line is drawn straight down form the COG of an object of any shape and if falls inside the base of support, it is in equilibrium.
• the ideal for increased stability: wide BOS and low COG

Question 12

Angular momentum

Answer 12

= rotational inertia x rotational velocity
- vector quantity (direction and magnitude)
- for an object that is small compared with the radial distance to its axis of rotation
= mvr OR Mass x velocity x radius

Question 13

Rotational version of Newton’s 1st law

Answer 13

An object or system of objects will maintain its angular momentum unless acted upon by an external net torque

Question 14

Conservation of angular momentum

Answer 14

If no external net torque acts on a rotating system, the angular momentum of that system remains constant
- therefore, with not external torque, the product of rotational inertia and rotational velocity at one time will be the same as at any other time