Question

Suppose a 5.7-gram quarter has the same coefficient of static friction between it and the turntable as does the penny? In what way will the speed at which it flies off differ from that of the penny?

Answer 1

linear velocity of the two currencies is the same since it does not depend on mass

Step-by-step explanation:

Let's solve the problem! To answer the question, let's start by writing Newton's equation for rotational motion.

τ = I α (1)

Torque is

τ = fr r

We are assuming that the two currencies enter the same distance from the pivot point

The friction force equation

fr = μ N

Let's write Newton's equation for the vertical axis

N - W = 0

We substitute in 1

μ m g r = I α

The angular and linear acceleration are related

a = α r

α = a / r

The acceleration is centripetal

a = v² / r

α = v² / r²

μ m g r = I v² / r²

If we assume that coins are like particles, their moment of inertia is

I = m r²

μ m g r = (m r²) v² / r²

μ g r = v²

v = √ μ g r

We can see that the linear velocity of the two currencies is the same since it does not depend on mass