How Does Gear Size Affect Torque in a Truck Transmission?

In summary: For part (b), use Newton's second law and the definition of torque. For part (c), use the same reasoning as part (b) but with the smaller central gear. For part (d), use the rotational kinematic equation to find the angular velocity and then convert to linear velocity. For part (e), consider the relationship between gear ratios and speed. In summary, the conversation discusses the use of compound gears within a truck and the calculations needed to determine moments of inertia, torque exerted by the driving gear, and the truck's speed.
  • #1
mahmoudnasr12
1
0

Homework Statement



PS:The compound gear to the right is located inside a truck, whose engine rotates the driving gear with torque of 816 N*m. Assume that in the figure to the right, each of the smaller gears have a radius of 5.0 cm, and the larger gears have a radius of 25cm. Also, assume that the two central gears are linked by a shared axle, so that they rotate together, and that all the axles are held in place (by forces of some unknown magnitude). You may treat the gears as solid cylinders with a thickness of 2.0cm, and a density of 8,050 kg/m^3. Also assume all the gears are moving at a constant angular velocity.
a) What are the moments of inertia of both the large and small gears?

b) Using Newton's Laws, deduce the magnitude of the torque exerted by the driving gear on the large central gear, assuming that there are no additional forces/torques (other than those mentioned and gravity) acting on the driving gear.

c)Using the same reasoning as in part (b), determine the torque exerted by the smaller central gear on the large gear to the right (again assuming there are no other forces acting on the central gears).

d) Assuming that the driving gear is rotating at 5000RPM, and that the large gear on the right is connected to the tires of the vehicle (30 cm radius), how fast is the truck moving (in mph)?

e)Assuming the truck has a four-speed transmission, what gear do you think the truck is in?.

Homework Equations


I= (1/2)mr^2
F=ma
τ=Fr
I=∑MR^2
and perhaps rotational kinematic equations

The Attempt at a Solution


I have no idea how to start this problem, could someone please help me start it? I would appreciate it.
 

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  • #2
Welcome to PF;
Start with the definition of moment of inertia for part (a).
 

Related to How Does Gear Size Affect Torque in a Truck Transmission?

What is the definition of rotation of rigid bodies?

Rotation of rigid bodies refers to the movement of an object around an axis or point, where all points on the object move in a circular path at the same time and with the same angular velocity.

How is rotation of rigid bodies different from translation?

Rotation involves the movement of an object around an axis or point, while translation involves the movement of an object from one location to another in a straight line.

What is the role of inertia in rotation of rigid bodies?

Inertia is the resistance of an object to change its state of motion. In rotation of rigid bodies, inertia plays a crucial role in determining the object's angular velocity and the amount of torque required to produce rotation.

What is the difference between angular velocity and angular acceleration?

Angular velocity refers to the rate at which an object is rotating around an axis or point, while angular acceleration refers to the rate at which the angular velocity is changing. In other words, angular acceleration measures how quickly an object's rotation is speeding up or slowing down.

How are moments of inertia and rotational kinetic energy related?

Moments of inertia, which depend on the mass distribution of an object, are directly proportional to the rotational kinetic energy of the object. This means that the larger the moment of inertia, the more rotational kinetic energy is required to produce rotation.

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