Physics Test Three

How you know that a 1D collision is occurring

Things are moving up/down or left/right

1D collision equation for when things end up separated

M₁V_1i + M₂V_2i = M₁V_1f + M₂V_2f

1D collision equation for when things stick together

M₁V_1i + M₂V_2i = (M₁ + M₂)V_f

How you know that something is a 2D collision

1. Something goes north/south

2. Something has angles

3. Something goes east/west

Steps to solve a 2D collision

1. M₁V_1x + M₂V_2x = (M₁ + M₂)V_f cos theta

2. M₁V_1y + M₂V_2y= (M₁ + M₂)V_f sin theta

3. Solve for V_f cos/sin theta

4. Divide by V_f sin theta on top of V_f cos theta and use tangent

5. Solve for theta and plug in

Impulse

Net force applied over a certain time or change in momentum (impulse is equal and opposite in collisions, e.g one car could be +45 and the other -45)

I = F(change in t) example

A baseball bat hitting a ball

I = m(change in velocity) example

A ball drops and then bounces back up

Combination of impulse equations

F(change in time) = m(V_f - V_i)

CCW is pos or neg? CW is pos or neg?

CCW is positive and CW is negative

How to get degrees to radians

multiply by 2pi/360

How to get revolutions to radians

multiply by 2pi

How to get rev/s to rad/s

multiply by 2pi

How to get rpm to rad/s

multiply by 2pi/ 60

Sliding (linear velocity) equation

K_t = ½ mv²

Rolling (angular velocity) equation

K_rot = ½ Iw²

Conservation of Energy equation

mgh_i + ½ mv_i² + ½ Iw_i² = mgh_f + ½ mv_f² + ½ Iw_f²

Rolling without slipping equation

½ mv_i² + ½ Iw_i² = ½ mv_f² + ½ Iw_f² + mgh

What to do if you know the height in a problem

1. Use K_total = K_t + K_rot

2. Make w² into v²/r²

3. Set the equation equal to mgh and solve for v

4. convert v to w using w=v/r

What to do if you know v or w at the bottom in a problem

1. If you know v, use K_t and for w, use K_rot

2. convert to the other velocity where v=rw or w=v/r

3. Calculate the K_t or the K_rot

4. Find the K_total

5. Use K_total = mgh to find the height

The three equations that torque (angular acceleration) could be equal to

1. = rFsintheta

2. = I(alpha)

3. = rF

In the torque equation, r represents…

The distance from the pivot to the force

In the torque equation, F represents…

The weight force or tension

In the torque equation, theta represents…

The angle between the r and F

In static equilibrium when the sum of torques equal zero, what are the steps to solving?

1. Pick a point of where it pivots (whatever the pivoting point is, the force disappears)

2. Locate all forces on the object

3. Calculate the distance from each force to the pivot (positives and negative matter)

4. Solve

Angular momentum equation when things are separated

I₁w_1i + I₂w_2i = I₁w_1f + I₂w_2f

Angular momentum equation when things end up together

I₁w_1i + I₂w_2i = (I_i + I₂)w_f