You hold a bucket in one hand, and in the bucket is a 500 g rock. You swing the bucket so the rock moves in a vertical circle 2.2 m in diameter. What is the minimum speed

3.28 m/s

Explanation:

From the question,

Applying newtons ,

F = mv²/r Equation 1

Where m = mass of the rock, v = speed, r = radius of the circle, F = Centriputal force.

But,

Centriputal force is equal to the weight of the rock

F = mg Equation 2

Equate equation 2 into equation 1

mg = mv²/r

Therefore,

v = √gr Equaion 3

Given: r = 2.2/2 = 1.1 m

Constant: g = 9.8 m/s²

Substitute into equation 3

v = √(9.8×1.1)

v = √(10.78)

v = 3.28 m/s

Hence the minimum speed is 3.28 m/s