Motorcycle horizontal acceleration-front wheel rise

In summary, the question is asking for the horizontal acceleration of a motorcycle that will cause the front wheel to rise off the ground. The solution involves setting the torque on the rear wheels equal to the torque on the center of mass, which happens when the weight is evenly distributed between the two wheels. This means that there is no rotational acceleration at this point in time, and the center of mass is accelerating forward.
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Motorcycle horizontal acceleration--front wheel rise

The distance between the centers of the wheels of a motorcycle is 171 cm. The center of mass of the motorcycle, including the rider, is 95.0 cm above the ground and halfway between the wheels. Assume the mass of each wheel is small compared to the body of the motorcycle. The engine drives the rear wheel only. What horizontal acceleration of the motorcycle will make the front wheel rise off the ground?

2. Homework Equations

τ=rFsinϕI understand that the solution is when .95ma=1.71/2(mg), so when the torques are set equal to each other. why though? thanks!
 
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All the weight is on the rear wheels. Acceleration of the center of mass is in the forward direction. Is there any rotational acceleration about the center of mass at this point in time?
 

1. What is motorcycle horizontal acceleration?

Motorcycle horizontal acceleration is the rate at which the motorcycle's speed changes in the horizontal direction. It is measured in meters per second squared (m/s²).

2. What is front wheel rise?

Front wheel rise, also known as wheelie, is when the front wheel of a motorcycle lifts off the ground due to a sudden increase in acceleration.

3. Why does the front wheel of a motorcycle rise?

The front wheel of a motorcycle rises due to the balance of forces acting on the bike. When the motorcycle accelerates rapidly, the force of the rear wheel pushing the bike forward can overcome the downward force of gravity, causing the front wheel to lift off the ground.

4. How does motorcycle horizontal acceleration affect front wheel rise?

Higher motorcycle horizontal acceleration can lead to a greater chance of front wheel rise, as the increased force from the rear wheel can cause the front wheel to lift off the ground more easily. This is why skilled riders are able to control their motorcycle's acceleration to prevent wheelies.

5. What are the potential dangers of front wheel rise?

The main danger of front wheel rise is loss of control of the motorcycle. If the front wheel stays off the ground for too long, it can result in a loss of balance and the rider falling off the bike. It can also lead to damage to the bike if it lands in an uncontrolled manner.

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