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Angular Motion in Cars Applying Physics of Rotational Motion, Newtons Laws and Kinematics to the motion of a car.

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Engine Speed An engine rotates with a given angular velocity as it cycles. The angular velocity is measured in RPMs. The tachometer is located on the instrument panel and it measures the engine speed. Engine speed in RPMs will be the independent variable of this simulation.

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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.

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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

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Drive Train of a Car Energy Transformations take place in the following order: Work done by pistons Rotating Crank Shaft Transmission Gears Drive Shaft and differential Axle and Tires

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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.

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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. 1 st Gear, highest ratio, most torque 5 th Gear, lowest ratio (on a 5 speed transmission), least torque

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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. r tire F tire F ground Newtons 2 nd Law Newtons 3 rd Law = -F ground F tire

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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!

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