Answer:
The torque required is 0.024Nm
Explanation:
Solution:
Data Given;
Mass of sphere = 80kg
Radius of sphere = 0.1m
Time = 5s
Angle = 1.5radians
To calculate the torque is required to twist and hold the sphere, we use the formula;
Torque = Inertia * angular acceleration -----------------------------1
where,
Inertia = 1/2 mr²---------------------------------------------------------------2
Substituting into the formula, we have
= 1/2 * 80*0.1²
= 1/2 * 0.8
= 0.4kgm²
Angular acceleration = angular velocity/time----------------------3
Where angular velocity = ∅/time
Substitution into equation 3, we have
= 1.5/5²
= 1.5/25
= 0.06rad/s²
Coming back to equation 1,
Substituting the values obtained into equation 1, we have
Torque = Inertia * angular acceleration
= 0.4 * 0.06
= 0.024Nm