Final answer:
The expression for the linear velocity of a rock of mass M attached to a massless string of length L and swung in a circle at N revolutions per minute when it is released is v = (2πNL)/60.
Step-by-step explanation:
The student is asking for an expression for the linear velocity of a rock of mass M attached to a massless string of length L when it is swung in a circle and then released. To determine this, we need to use the relationship between angular velocity and linear velocity. The rock swung in a circle at a velocity of N revolutions per minute (rpm) has an angular velocity, which can be converted to radians per second. This angular velocity (ω) can be used to find the linear velocity (v) at the point of release.
The angular velocity in radians per second is given by ω = 2πN/60, considering there are 2π radians in one revolution and 60 seconds in one minute. The linear velocity at the circumference of the circle made by the rock is directly proportional to the angular velocity and the length of the string which acts as the radius (L) of the circle. The formula is v = ωL.
Substituting the expression for angular velocity into the equation for linear velocity, we get:
v = (2πN/60)L
Therefore, the expression for the linear velocity of the rock at the moment it is released is:
v = (2πNL)/60