Question

the period (time for one circle) in case a is twice that of case b. the circles radius is the same in each case. how does the speed in case a compare to the speed in case b? the speed in case a is... ... the speed of case b.

Explanation:

Step1: Recall the formula for speed in circular motion

The speed \(v\) in circular motion is given by \(v=\frac{2\pi R}{T}\), where \(R\) is the radius of the circle and \(T\) is the period.

Step2: Calculate the speed for Case A

For Case A, \(T_A = 2T\) and \(R_A=R\). So, \(v_A=\frac{2\pi R}{2T}=\frac{\pi R}{T}\).

Step3: Calculate the speed for Case B

For Case B, \(T_B = T\) and \(R_B = R\). So, \(v_B=\frac{2\pi R}{T}\).

Step4: Compare \(v_A\) and \(v_B\)

Divide \(v_A\) by \(v_B\): \(\frac{v_A}{v_B}=\frac{\frac{\pi R}{T}}{\frac{2\pi R}{T}}=\frac{1}{2}\).

Answer:

The speed in Case A is half the speed of Case B.