Physics 207 Unit 1

Two formulas for dot product

Gives a scalar

ABCos(theta) → thetais the angle between vectors A and B when placed tail to tail

AxBx +AyBy +AzBz

Formulas for cross product

Gives a vector

ABSin(theta)

Cx= AyBz - AzBy

Cy= AzBx-AxBz

Cz= AxBy-AyBx

T or F: the magnitude of a vector is independent of the coordinate system used?

T!

When is the dot product of two vectors 0?

When theta is 90^o

What does the dot product tell us?

How well two vectors project onto each other.

Does a car moving with uniform circular motion have an acceleration? Why or why not

Yes! Because the direction of their velocity vector changes with time, therefore there MUST be an acceleration. With UCM, acceleration is always perpendicular to the track and has a constant magnitude. This is called the centripetal acceleration.

What is the equation for centripetal acceleration?

a_c = w²r OR a_c=v²/r

How does an object’s acceleration change if its speeding up while moving in a circle?

It’s total acceleration now has both a centripetal and tangential component. These two components are always perpendicular to each other.

TOF for a projectile equation

T= 2v_isin(theta_initial)/g

Range of projectile equation

R=v_i²sin(2theta)/g

You’ll get the max range of a projectile when your initial angle is …?

45^o

What is the formula for arc traversed?

s = r(theta) or s=(theta_f-theta_i)r

derive the rw equation for angular velocity

1. v = ds/dt s= arc traversed

2. s=theta*r, so d(theta*r)/dt

3. d(theta)/dt =w, SO, rw=v

Period (T) equation and frequency equation

T= 2pi/w = 2pir/v

Frequency (F) =1/T

Tangential acceleration is __ to instantaneous velocity

Parallel

What do floor scales measure?

The normal force you exert on it, which by Newton’s third law, is the same magnitude of the normal force it exerts on you. It does NOT measure F_g(weight)!!!