PHYS 218 Exam 1

2D movement (x,y graph)

• Velocity is always tangent to path
• Acceleration points to concave side of a curve

1D movement (x,t graph)

• Velocity is slope of line tangent
• Acceleration: sign is determined by concavity (<0 cc↓, =0, >0 cc↑)

Equations of motion

General Acceleration

$x(t)=x_{0}+\int _{0}^{t}v(t)\ dt$

$v(t)=v_{0}+\int _{0}^{t}a(t)\ dt$

Constant Acceleration

$x(t)=x_{0}+v_{0}t+{\frac {a}{2}}t^{2}$

$v(t)=v_{0}+at$

Extra (derived) equations

${v(t)}^{2}={v_{0}}^{2}+2ax(x(t)-x_{0})$

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x(t)-x_0 = \left(\frac{v_0+v(t)}{2}\right) t}

Circular Motion

Uneven Speed

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a_\perp = \frac{v^2}{R}} Changes direction of movement, but keeps speed of object

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a_\parallel = \frac{dv}{dt}} Changes speed of object, but keeps direction.

Constant Speed

Period (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle T} ) = time needed for 1 revolution

Frequency (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f} ) = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{T}}

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a_\parallel = 0}

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle |v| = \frac{2 \pi R}{T}}

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a_\perp = \frac{4 \pi^2 R}{T^2} = 4 \pi^2 R f^2}