AH Rotational Dynamics Questions

1. a) What is meant by the term ‘Torque’? b) What units are used to measure Torque? c) State the equation for Torque, listing the quantities and units involved. d) Describe the difference in effort required to loosen wheel nuts in a car when using a long and short torque wrench and explain this in terms of the ‘effective torque’ created. 2. a) What is meant by the term ‘Inertia’? b) What units are used to measure the Moment of Inertia of an object? c) State the two equations for the Moment of Inertia of a uniform circular disc (e.g a DVD) and a hoop (e.g a bicycle wheel with very light spokes). 3. Newton’s Second Law of Motion states F = ma.

a) State the angular equivalent of this equation.

b) State the quantities and units used in this angular equation.

c) What is required to produce an angular acceleration? 4. Linear momentum is given by the equation p = mv.

a) Use p = mv to prove that angular momentum L = Iω.

b) State the quantities and units used in the angular momentum equation.

c) State the law of conservation of angular momentum. 5. a) Which two quantities are required to work out the rotational kinetic energy? b) State the equation for rotational kinetic energy, listing all of the quantities and units involved.

6. A uniform circular disc of mass 4kg and diameter 50cm is rotating about its centre with a constant angular velocity of 10rads-1.

a) Calculate the angular momentum of the disc.

b) An identical disc is placed gently on top of the original disc. Calculate the new angular velocity of the system.

c) The top disc is then raised without disturbing the lower disc. What is the angular velocity of the lower disc?

d) A ring of the same mass and diameter is then gently placed to fit over the disc. Calculate the angular velocity of the disc and the ring.

7. Calculate the Rotational Kinetic Energy of each part of Q6. 8. A 4kg bicycle wheel of diameter 1.5m has a constant force of 30N applied (perpendicular to the spoke), 50cm from the centre. Calculate or find:

a) Angular acceleration.

b) Angular velocity after 4 seconds.

c) Linear velocity after 4 seconds on the rim of the wheel.

d) Number of revolutions made in 4 seconds.

e) Work Done in 4 seconds. 9. When 100J of work is done on a flywheel, its angular velocity increases from 60rpm to 150rpm. Calculate or find:

a) Angular velocities above converted into rads-1.

b) Moment of Inertia of the flywheel.

c) Rotational Kinetic Energy before and after work is done on the flywheel.

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13. (Radius of the disc = 58.0mm)

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