How Do You Calculate Bicycle Speed and Friction in Circular Motion?

AI Thread Summary
To calculate bicycle speed and friction in circular motion, the discussion focuses on a scenario where a bicycle travels in a circle with a radius of 20 m and a resultant force at a 15-degree angle with the vertical. The key equations mentioned are a = V^2/r and F = mrω^2, but the challenge lies in determining the angular velocity (ω) and acceleration (a) without additional information. The conversation suggests using the rotational force equation, Mv^2/r, to derive an expression for the frictional force. Additionally, the problem introduces a scenario where the frictional force is half its maximum value, prompting a calculation of the coefficient of static friction. Understanding these relationships is essential for solving the problem effectively.
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Suppose you ride a bicycle on a horizontal surface in a circle with a radius of 20 m. The resultant force exerted by the road on the bicycle (normal force plus frictional force) makes an angle of 15 degs with the vertical.
a. What is your speed?
b. If the frictional force is half its maximum value, what is the coefficient of static friction?

The problem is I got 2 equations that i can think of to solve for a). One equation is a=V^2/r and the other is F=mrw^2. But for the second equation I don't know the w(angular vel) and for the first I don't know a(acceleration). So how do I solve this?
 
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Your rotational force is
\frac{Mv^2}{r}
Can you use this to find an expression for your frictional force? (hint: no math needed)
 

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