The shaft of a turbine has a moment of inertia of 14 kg m² about its centre, while each of the three turbine blades has a moment of inertia of 6 kg m², relative to the centre of rotation of the turbine. What torque must be applied to the turbine to achieve an angular acceleration of 3 rad/sec²?

Give your answer in N.m to at least 2 significant figures

A unicylist is riding down the Princes Highway at a constant velocity. The free body diagram of his wheel is shown below. The rider is applying a torque (360 N.m) to the 0.5 m radius wheel which is opposed by the friction force Fr. If the coefficient of static friction is 0.6, and the coefficient of kinetic friction is 0.2, what is the combined mass of the wheel and rider?

Assume the wheel is not slipping (but would slip if any additional torque were applied), and assume gravitational acceleration is 9.81 m/s². Give your answer in kg to the nearest whole number.

A similar situation occurs, but this time, the adult pushes downwards on an angle with the same force.

Assume the pushing action is at an angle of 60 degrees from the horizontal, that the chain remains taut, and that the force is applied instantaneously. Find the applied torque, and give your answer in N.m to the nearest whole number.

A small child of mass 32 kg is sitting on a playground swing. The child's centre of mass is 2.2 metres from the pivot point of the swing. If the child is pushed by an adult applying 80 N of force as shown in the diagram, what torque will be applied to the child?

Assume the pushing action is perpendicular to the chain, that the chain remains taut, and that the force is applied instantaneously. Give your answer in N.m to the nearest whole number.

Which of the following statements is true regarding the moment of inertia? There may be more than one correct answer.

What is the moment of inertia of a thin rod of mass 0.3 kg rotating about its centre, if the distance from the end of the rod to its centre is 1.3 m? Give your answer in kg.m² to at least 3 significant figures.

The pendulum consists of a 4-kg circular plate and a 2-kg slender rod. Determine the moment of inertia of the pendulum about an axis perpendicular to the page and passing through point O.

What is the moment of inertia of a thin rod of mass 0.6 kg rotating about its centre, if the distance from the end of the rod to its centre is 2.2 m? Give your answer in kg.m² to at least 3 significant figures.

A thin disc and a thing ring both have the same mass and radius. Both rotate about the axes through their centre of mass and are perpendicular to their surfaces. If both of those have the same angular velocity, which of the following statement is true?

Given the spring and damping coefficients from the previous question remain unchanged, what would the mass need to be for the system to be critically damped?