Chapter 1: Kinematics and Dynamics

Question 1

Unit of mass in the imperial system? Therefore, imperial unit of force? Metric unit of force?

Answer 1

Slug. (slug * foot) /(second^2)

Newton: kg*m/s^2

Question 2

Simplifications for:
sin0? cos0? tan0?
sin30? cos30? tan30?
sin45? cos45? tan45? 
sin60? cos60? tan60?
sin90? cos90? tan90?

Answer 2

0, 1, 0
1/2, (sqrt3)/2, (sqrt3)/3
(sqrt2)/2, (sqrt2)/2, 1
(sqrt3)/2, 1/2, sqrt3 
1, 0, infinity

Question 3

How to find the resultant of multiple vectors?

Answer 3

1. break into X and Y components
2. add up each components to get resultant X and Y
3. use pythagorean theorem
4. find direction by using theta = inverse tan (opp/adj)

Question 4

What happens when you multiply a scalar by a vector?

Answer 4

Vector increases in magnitude and either points in the same direction or in the exact opposite direction (if the scalar is negative)

Question 5

How do you multiply two vectors to get a scalar quantity, like work (force times displacement)? (dot product)

Answer 5

A . B = |A| |B| cos theta

theta is the angle between the two vectors (90 if one is just an x quantity and the other is just a y)

Question 6

How do you multiply two vectors to get a third vector, like torque? (cross product)

Answer 6

A x B = |A| |B| sin theta

use right hand rule to determine direction of resultant: thumb is A, fingers are B, palm points in direction of C

Question 7

Difference between instantaneous velocity and instantaneous speed?
Between average velocity and average speed?

Answer 7

Same magnitude.

Different, as speed takes distance traveled into account whereas velocity accounts for displacement

Question 8

Formula for gravitational force?

Answer 8

F = Gm1m2/r^2,
where G is the universal gravitational constant (6.67E-11), m1 and m2 are the two object masses and r is the radius between them. Simplify G to 20/3E-11

Question 9

Equation for static friction? (resting object)

Answer 9

0 less than equal to (F_s) less than equal to (U_s *N)

Where F_s is static friction, U_s is the coefficient of static friction and N is the normal force (force pushing up from ground). Can be anywhere in that range from zero to right side of equation

Question 10

Equation for kinetic friction?

Answer 10

F_k = U_k*N

Where U_k is the coefficient of kinetic friction and N is the normal force. U_k is always smaller than U_s

Question 11

Force of gravity equation? (weight)

Answer 11

F_g = mg, where m is mass in kg and g is acceleration due to gravity = 9.8m/s^2 (round to 10)

Question 12

Acceleration formula?

Answer 12

change in velocity over change in time

Question 13

Newton’s first law? Equation?

Answer 13

A body at either at rest or in motion with constant velocity will remain that way unless a net force acts on it. F_net = ma = 0

Question 14

Newton’s second law? equation?

Answer 14

An object with mass m will accelerate when the vector sum of the forces results in some nonzero resultant force vector. F_net = ma

Question 15

Newton’s third law? Equation?

Answer 15

To every action there is an opposed but equal reaction.

F_ab = -F_ba

Question 16

What constitutes linear motion?

Answer 16

When an object’s velocity and acceleration are in the same direction

Question 17

Equations which describe linear motion? (4 of these badboys, know them for all the kinematics problems)

Answer 17

1. V = V_o + at
2. x = V_o*t + a(t^2)/2
3. v^2 = V_o^2 + 2ax
4. x = v!t

where x (or y), v and a are the displacement, velocity and acceleration vectors, V_o is initial velocity, v! is average velocity (really has a line over it not an !), and t is time

Question 18

Conditions for a free-fall problem?

Answer 18

No air-resistance, acceleration is 9.8m/s^2, and no terminal velocity

Question 19

What constitutes projectile motion?

Answer 19

Motion that follows a path along 2 dimensions. Velocity and acceleration are in the two directions (usually horizontal and vertical) and must be separated from one another. Horizontal velocity typically remains constant, while vertical velocity is accelerated downward due to gravity

Question 20

How to find vertical and horizontal velocity of an object launched at an angle (ex 37 degrees at 50m/s)

Answer 20

V_oy = 50sin37 = 50*0.6 = 30 
V_ox = 50cos37 = 50*0.8 = 40

Question 21

How do you divide inclined plane questions into horizontal and vertical force vectors due to gravity?

Answer 21

F_gparallel = mg(sin theta)
F_gperpendicular = mg(cos theta)

Question 22

In uniform circular motion, where is the instantaneous velocity? Where does centripetal force point?

Answer 22

Tangent to the circular path. Towards the center of the circle

Question 23

Equation that describes circular motion?

Answer 23

F_c = m(v^2)/r

where F_c is centripedal force, m is the mass, v is the speed and r is the radius

Question 24

In rotational equilibrium, what is the lever arm?

Answer 24

The distance between the applied force and the fulcrum (pivot point)

Question 25

Equation for torque?

Answer 25

torque = r x F = rF sin theta

where r is the length of the lever arm, F is the magnitude of the force, and theta is the angle between the lever arm and the force vectors (90 when flat)

Question 26

Postive vs negative torque?

Answer 26

clockwise is negative, counterclockwise is positive