A coin with a diameter of 1.9 cm is dropped on edge onto a horizontal surface. The coin starts out with an initial angular speed of 19 rad/s and rolls in a straight line without slipping. The rotation slows with an angular acceleration of magnitude 2.1 rad/s2.

What is the initial linear velocity of the coin?

linear velocity= w*r

What is the magnitude of the linear acceleration

How far does the coin roll before it stops?

To determine the initial linear velocity of the coin, we can use the relationship between linear velocity and angular velocity for a rolling object.

When a solid object rolls without slipping, the linear velocity of any point on the object's circumference is equal to the product of its angular velocity and the radius of the object. In this case, the coin is rolling on its edge, so we need to consider the radius of the coin.

The radius of the coin can be found by dividing its diameter by 2:
Radius = Diameter / 2 = 1.9 cm / 2 = 0.95 cm = 0.0095 m

The formula to calculate linear velocity is:
Linear velocity = Angular velocity * Radius

Given:
Angular velocity (ω) = 19 rad/s
Radius (r) = 0.0095 m

Using the above formula, we can calculate the initial linear velocity of the coin:
Linear velocity = 19 rad/s * 0.0095 m = 0.1805 m/s

Therefore, the initial linear velocity of the coin is 0.1805 m/s.