A shaft made of aluminum has a diameter of 60 mm and is subjected to a torque of 200 Nm. Determine the angle of twist at the free end of the shaft, given that the
modulus of rigidity for aluminum is 25 GPa.
To calculate the angle of twist at the free end of the shaft, we can use the formula:
θ = T*L / (G*J)
Where:
θ = angle of twist (in radians)
T = torque applied to the shaft (in Nm)
L = length of the shaft (in meters)
G = modulus of rigidity (in Pa)
J = polar moment of inertia of the shaft
First, we need to calculate the polar moment of inertia of the shaft. Since the shaft is circular, the polar moment of inertia can be calculated using the formula:
J = π*(d^4) / 32
Where:
d = diameter of the shaft = 60 mm = 0.06 m
J = π*(0.06^4) / 32
J = π*0.00000216 / 32
J = 0.00000006746 m^4
Now substitute the given values into the formula for the angle of twist:
θ = 200 Nm * L / (25 GPa * 0.00000006746 m^4)
We don't have the length of the shaft provided in the question, so we cannot calculate the angle of twist without it.