Question

a cyclist is riding around a circular track. if the cyclist increases their speed, what happens to the centripetal acceleration?
a) the centripetal acceleration decreases
b) the centripetal acceleration stays the same
c) the centripetal acceleration increases
d) the centripetal acceleration becomes zero

Explanation:

Step1: Recall the formula for centripetal acceleration

The formula for centripetal acceleration \(a_c\) is \(a_c=\frac{v^{2}}{r}\), where \(v\) is the speed of the object moving in a circular path and \(r\) is the radius of the circular path.

Step2: Analyze the effect of increasing speed

If the radius \(r\) of the circular track remains constant (since it's the same track) and the speed \(v\) is increased. Let the initial speed be \(v_1\) and the final speed be \(v_2\) such that \(v_2>v_1\). The initial centripetal acceleration \(a_{c1}=\frac{v_{1}^{2}}{r}\) and the final centripetal acceleration \(a_{c2}=\frac{v_{2}^{2}}{r}\). Since \(v_{2}^{2}>v_{1}^{2}\) (because \(v_2 > v_1>0\)), then \(\frac{v_{2}^{2}}{r}>\frac{v_{1}^{2}}{r}\).

Answer:

c) The centripetal acceleration increases