A constant torque of 20 N.m is applied to a wheel pivoted on a fixed axis. At what rate is power being furnished to the wheel when it is rotating at 0.5 rev/sec?
P = torque* w
w = .5 * 2 pi radians/s = pi radians/s
P = (20 * pi) watts
To find the rate at which power is being furnished to the wheel, we need to determine the angular velocity of the wheel and then use the formula for power.
First, let's convert 0.5 rev/sec to radians/sec:
1 revolution (rev) = 2π radians
Therefore, 0.5 rev = 0.5 * 2π radians = π radians
Now, we need to calculate the angular velocity (ω) in radians/sec:
ω = 0.5 rev/sec * 2π radians/rev = π radians/sec
Next, we can use the formula for power (P) in terms of torque (τ) and angular velocity:
P = τ * ω
Given that the torque (τ) is 20 N.m and the angular velocity (ω) is π radians/sec, we can substitute these values into the formula:
P = 20 N.m * π radians/sec
Now, let's calculate the power (P):
P = 20 N.m * π radians/sec ≈ 62.83 N.m/s or 62.83 Watts
Therefore, the power being furnished to the wheel when it is rotating at 0.5 rev/sec is approximately 62.83 Watts.