Question

You rev your car's engine and watch the tachometer climb steadily from 1400 rpm to 5400 rpm in 3.1 s. (a) What is the angular acceleration of the engine? rad/s2 (b) What is the tangential acceleration of a point on the edge of the engine's 3.5 cm diameter crankshaft? m/s2 (c) How many revolutions does the engine make during this time? rev

Answer 1

a)

Angular acceleration is

$\alpha =\frac{\Delta w}{\Delta t}$

= (5400-1400)(2pi/60) / 3.1 = 135.12 rad/s^2

b)

tangential acceleration is

$a_{t}=\alpha r$

= 135.12 * 3.5*10^(-2) / 2 = 2.365 m/s^2

c)

$\Delta \Theta =w_{0}t+\frac{\alpha t^{2}}{2}$

where w0 is initial speed = 1400*2pi/60 = 146.61 m/s

$\Delta \Theta =$ 146.61*3.1 + 135.12*(3.1^2)/2

= 1103.74 rad = 1103.74/2pi = 175.67 rev