3. Mechanics Part 2

Question 1

What is an objects center of mass?

Answer 1

It is the location of an object where an applied force would push the object in the direction of that force. Any force applied outside of the center of mass would cause some kind of rotational movement.

Question 2

What is the formula for center of mass? How do you use it?

Answer 2

To find a systems center of mass…

x = ((m1x1) + (m2x2) + (m3x3)) / m1 + m2 + m3

We must assign some reference point of 0. Typically, we assign the furthest left object as 0 and measure out x of all other objects relative to this. When choosing the answer, remember what reference point you chose.

Question 3

What is centripetal acceleration?

Answer 3

Centripetal acceleration is the acceleration any object feels that is in uniform circular motion. Centripetal acceleration always points towards the center of the circle.

Question 4

What is the formula for centripetal acceleration?

Answer 4

ac = v^2 / r

Question 5

t or f, Fnet and a always point in the same direction.

Answer 5

True, (an object is always accelerating in the direction of the force applied). Thus, in UCM, Fnet points towards the center of the circle like ac.

Question 6

What is the formula of the centripetal force?

Answer 6

F = ma

ac = v^2 / r

Fc = (mv^2) / r

Question 7

What is 1 revolution of a circle?

Answer 7

One full length around a circle, which is equal to 2π radians.

Question 8

What is the centripetal force?

Answer 8

The centripetal force is the Fnet acting on an object in uniform circular motion. There is no unique force called Fc, but rather the sum of other forces (such as gravity, tension, etc.)

Therefore, we DO NOT include Fc in a force diagram

Question 9

If a satellite is orbiting earth at a constant speed, what is the centripetal force?

Answer 9

The only force is earths gravitational pull. Therefore, Fc = Fg.

We can say that (GMm) / r^2 = mv^2/r
thus,
GM / r = v^2

This is how you find the speed of a satellite

Question 10

If we increase the radius of an object spinning in UCM, what happens to the centripetal acceleration?

Answer 10

ac = v^2 / r

increasing radius actually still increases ac. This is because velocity is proportional with radius (and it is squared). So increasing radius substantially increases velocity, and in turn, ac increases.

Question 11

What is the formula for torque?

Answer 11

T = rFsinϴ

note that sin(90) = 1. Therefore, when F and r are perpendicular, torque is at its maximum

Question 12

t or f, only the perpendicular component of an applied force contributes to torque.

Answer 12

true, this is evident in its formula which only considers sinϴ.

Question 13

t or f, its customary to call counter-clockwise torque positive and clockwise torque negative.

Answer 13

True, however, when calculating it does not really matter.

Question 14

what are the units of torque?

Answer 14

The newton-meter. Note that this is actually the same unit as work.

Question 15

When calculating torque, what is the lever arm?

Answer 15

If torque is applied at an angle other than 90 degrees, the lever arm is the perpendicular point that meets the forces line of action and the pivot point of rotation.

The lever arm is always perpendicular to the applied force and thus

T = LF

Question 16

What is static and dynamic equilibrium?

Answer 16

equilibrium always means zero acceleration. Static equilibrium means zero velocity, dynamic equilibrium means constant velocity.

Question 17

What is the difference between rotational and translation al equilibrium?

Answer 17

transnational equilibrium = the forces all cancel out

rotational equilibrium = the torques all cancel out

Question 18

rotational equilibrium means net torque is zero which means CCW = CW, t or f,?

Answer 18

True, we can set all opposing torques as equal to each other.

Question 19

What is rotational inertia?

Answer 19

Rotational inertia (I) is how resistant an object is to rotational acceleration (α).

T = I x α
(inertia times acceleration).

Question 20

How can two objects with the same mass have different rotational inertia values?

Answer 20

Rotational inertia is dependent on both mass and the distance the object is from the axis of rotation. An object that is very far from the fulcrum will have MORE rotational inertia than an object that is close to the fulcrum.

Question 21

Why does a hollow ball have increased rotational inertia compared to a solid ball of the same size and mass?

Answer 21

T = I x α

rotational inertia depends on mass and the distance an object is from the rotational axis. In a hollow ball, all of the mass is at a distance of r from the rotational axis. In contrast, a solid ball, on average, has its mass closer to the rotational axis. Thus, the hollow ball has more inertia and requires increased torque to generate the same acceleration.