The crankshaft in your car engine is turning at a frequency of 3000 rpm. What is the shafts angular speed?
w = 2πf
To convert from rotations per minute (rpm) to angular speed, we can use the following formula:
Angular speed (ω) = 2π × Frequency
Given that the frequency of the crankshaft is 3000 rpm, we can substitute this value into the formula:
Angular speed (ω) = 2π × 3000 rpm
Now, let's calculate the angular speed:
Angular speed (ω) = 2π × 3000 rpm
≈ 2π × 3000 × (1 min / 60 sec) [Converting minutes to seconds]
≈ 2π × 50 sec⁻¹
Therefore, the angular speed of the crankshaft is approximately 100π radians per second (rad/s).
To find the angular speed of the crankshaft, we need to convert the given speed from revolutions per minute (rpm) to radians per second (rad/s).
First, we need to know the conversion factor between rpm and rad/s. Since one revolution is equal to 2π radians, the conversion factor is:
1 rpm = 2π rad/min
To convert from minutes to seconds, we need to divide by 60, so the conversion factor becomes:
1 rpm = (2π/60) rad/s
Now that we have the conversion factor, we can calculate the shaft's angular speed:
Angular speed (ω) = Crankshaft speed (in rpm) x Conversion factor
ω = 3000 rpm x (2π/60) rad/s
ω = 3000 x (2π/60) rad/s
ω = 100π rad/s
ω ≈ 314.16 rad/s
Therefore, the angular speed of the crankshaft is approximately 314.16 rad/s.