Angular Motion in Cars

Applying Physics of Rotational Motion, Newton’s Laws and

Kinematics to the motion of a car.

Engine Speed

• An engine rotates with a given angular velocity as it cycles.

• The angular velocity is measured in RPM’s.

• The tachometer is located on the instrument panel and it measures the engine speed.

• Engine speed in RPM’s will be the independent variable of this simulation.

Combustion Cylinders

• A combustion cylinder with a movable piston is where fuel is converted to mechanical energy

• It takes in a fuel-air mixture which is ignited exothermically by a spark from the spark plug.

• The pressure pushes the piston inside the cylinder doing work to the main drive shaft of the car.

Transferring Motion to the Wheels

• The angular velocity of the engine is not equal to the angular velocity of the wheels of the car (although they are proportional)

• As energy is transferred through gears the torque ( and angular velocity vary inversely

as

Drive Train of a Car

• Energy Transformations take place in the following order:

Gear Ratios

• Different gears are used in the transmission to either increase or decrease the angular velocity of the wheels compared to the engine speed.

• The ratios of the gears combined with the engine speed can be used to predict the velocity of the car if the gear is known.

• The gear ratio is how many times the engine must rotate for that gear to rotate.

Gear Ratios

• Higher gear ratio means more torque and slower rotational speed at the tires.

• Lower gear ratio means less torque but higher rotational speed at the tires.

• 1st Gear, highest ratio, most torque

• 5th Gear, lowest ratio (on a 5 speed transmission), least torque

Relating Transmission Torque () to Acceleration of the Car

• The force generated at the tires depends on the torque at the wheels and the radius of the tires.

wheeltire

tire

Fr

tirescar

car

Fa

m rtireFtire

Fground

Newton’s 2nd Law

Newton’s 3rd Law= -FgroundFtire

Timing the Acceleration

• Once the acceleration is known the car can be accelerated from rest.

• The gear will determine the torque from the table given and the time to reach a given speed can be calculated using equations of motion.

• Open Excel and get started!