10.7 Newton’s Second Law for Rotation

The fan blades on a jet engine have a moment of inertia $30.0 \left( \text{kg}-\text{m}\right)^{2}$. In 10 s, they rotate counterclockwise from rest up to a rotation rate of 20 rev/s. (a) What torque must be applied to the blades to achieve this angular acceleration? (b) What is the torque required to bring the fan blades rotating at 20 rev/s to a rest in 20 s?

A rod is pivoted about one end. Two forces $\overset{\rightarrow}{F} \textrm{ } \textrm{ } \textrm{ } \text{and} - \overset{\rightarrow}{F}$ are applied to it. Under what circumstances will the rod not rotate?

Suppose you exert a force of 180 N tangential to a 0.280-m-radius, 75.0-kg grindstone (a solid disk). (a)What torque is exerted? (b) What is the angular acceleration assuming negligible opposing friction? (c) What is the angular acceleration if there is an opposing frictional force of 20.0 N exerted 1.50 cm from the axis?

A constant torque is applied to a rigid body whose moment of inertia is $4.0 \left( \text{kg}-\text{m}\right)^{2}$ around the axis of rotation. If the wheel starts from rest and attains an angular velocity of 20.0 rad/s in 10.0 s, what is the applied torque?

A flywheel ($I = 100.0 \left( \text{kg}-\text{m}\right)^{2}$) rotating at 500.0 rev/min is brought to rest by friction in 2.0 min. What is the frictional torque on the flywheel?

Suppose when Earth was created, it was not rotating. However, after the application of a uniform torque for 6 days according to the current length of a day, it was rotating at 1 rev/day. (a) What was the angular acceleration during the 6 days? (b) What torque was applied to Earth during this period? (c) What force tangent to Earth at its equator would produce this torque?