(II) A coin is placed 12.0 cm from the axis of a rotating turntable of variable speed. When the

step 1 So we have a coin that's paced 12 centimeters from the axis of a rotating turn table. That 12 ce

(II) A coin is placed 12.0 cm from the axis of a rotating...

(II) A coin is placed 12.0 $\mathrm{cm}$ from the axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 35.0 rpm (revolutions per minute) is reached, at which point the coin slides off. What is the coefficient of static friction between the coin and the turntable?

(II) A coin is placed 12.0 $\mathrm{cm}$ from the axis of a rotating
turntable of variable speed. When the speed of the turntable
is slowly increased, the coin remains fixed on the turntable
until a rate of 35.0 rpm (revolutions per minute) is reached,
at which point the coin slides off. What is the coefficient of
static friction between the coin and the turntable?

Key Concepts

Uniform Circular Motion

Uniform circular motion refers to the movement of an object along a circular path at a constant speed. Even though the speed remains constant, the direction of the object's velocity changes continuously, which requires a net force to act towards the center of the circle. This concept is key in analyzing the dynamics of objects in rotational systems, such as a coin on a turntable.

Centripetal Force

Centripetal force is the inward force required to keep an object moving in a circular path. In the context of a rotating turntable, it is this force that acts towards the center of the rotation, ensuring that the coin follows a curved trajectory. The magnitude of the centripetal force needed increases with both the speed of the rotation and the radius of the circular path.

Static Friction

Static friction is the frictional force that resists the initiation of sliding motion between two surfaces. Its maximum value, defined by the coefficient of static friction multiplied by the normal force, determines the threshold at which an object, such as a coin on a rotating turntable, will begin to slide. When the required centripetal force exceeds this maximum static friction force, the object can no longer remain fixed on the surface.

Rotational Kinematics and Unit Conversion

Rotational kinematics deals with the angular aspects of motion, including quantities such as angular speed and acceleration. In problems involving rotations, it is often necessary to convert units like revolutions per minute (rpm) to radians per second to accurately calculate forces and accelerations. This conversion is critical for applying the formulas of circular motion in a consistent unit system.

Transcript

Please give Ace some feedback