Worksheet: Work and Power for Rotational Motion

In this worksheet, we will practice applying the work–energy theorem and principle of energy conservation using the quantities associated with rotational motion.

Q1:

A wind turbine rotates at 20 rpm. If its power output is 2.0 MW, what is the torque produced on the turbine from the wind?

  • A 1 0 × 1 0 N⋅m
  • B 1 1 × 1 0 N⋅m
  • C 9 . 5 × 1 0 N⋅m
  • D 9 . 2 × 1 0 N⋅m
  • E 9 . 0 × 1 0 N⋅m

Q2:

A uniform cylindrical grindstone has a mass of 10 kg and a radius of 12 cm.

What is the rotational kinetic energy of the grindstone when it is rotating at 1.5×10 rpm?

After the grindstone’s motor is turned off, a knife blade is pressed against the outer edge of the grindstone with a perpendicular force of 5.0 N. The coefficient of kinetic friction between the grindstone and the blade is 0.80. Use the work energy theorem to determine how many turns the grindstone makes before it stops.

Q3:

A propeller is accelerated from rest to an angular velocity of 1,000 rpm over a period of 6.00 seconds by a constant torque of 2.00×10 N⋅m.

What is the moment of inertia of the propeller?

What power is being provided to the propeller 3.00 s after it starts rotating?

Q4:

On a frictionless inclined plane, a block of mass 2.0 kg is attached by a cord to a pulley of mass 1.0 kg and radius 20 cm, as shown.

What is the acceleration of the block down the plane?

What is the work done by the gravitational force to move the block 50 cm?

Q5:

A clay cylinder of radius 10.0 cm on a potter’s wheel spins at a constant rate of 30.0 rev/s. The potter applies a force of 12 N to the clay with his hands and the coefficient of friction is 0.15 between his hands and the clay.

What is the power that the potter has to deliver to the wheel to keep it rotating at this constant rate?

Q6:

An athlete in a gym applies a constant force of 45.0 N to the pedals of a bicycle to keep the rotation rate of the wheel at 15.0 rev/s. The length of the pedal arms is 20.0 cm.

What is the power delivered to the bicycle by the athlete?

Q7:

A solid sphere of mass 48 kg is rolling in a straight line at a speed of 6.0 m/s across a horizontal surface. What is the magnitude of the work required to bring the sphere to rest?

Q8:

A string wrapped around a pulley is pulled by a constant force F of 50 N directed vertically downward, as shown in the diagram. The pulley’s radius 𝑅=0.10m and its moment of inertia is 2.5×10 kg⋅m2. The string does not slip as it is pulled. Starting from rest, what is the angular speed of the pulley after 1.0 m of string has been unwound from it?

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