A child places a picnic basket on the outer rim of a...

A child places a picnic basket on the outer rim of a merry-go-round that has a radius of 4.6 $\mathrm{m}$ and revolves once every 30 $\mathrm{s}$ . (a) What is the speed of a point on that rim? (b) What is the lowest value of the coefficient of static friction between basket and merry-go-round that allows the basket to stay on the ride?

A child places a picnic basket on the outer rim of a merry-go-round that has a radius of 4.6 $\mathrm{m}$ and revolves once every 30 $\mathrm{s}$ .
(a) What is the speed of a point on that rim? (b) What is the lowest
value of the coefficient of static friction between basket and
merry-go-round that allows the basket to stay on the ride?

Key Concepts

Uniform Circular Motion

This concept involves an object moving in a circular path at a constant speed. Although the speed is constant, the direction changes continuously, which means the object is accelerating. Uniform circular motion is characterized by parameters such as radius, period (or frequency), and the resulting tangential speed.

Period and Tangential Speed Relationship

The tangential speed of an object in circular motion is directly related to the circumference of the circle and the period over which one complete revolution occurs. The relationship is given by the formula v = (2?r) / T, where v is the speed, r is the radius of the circle, and T is the period.

Centripetal Force and Acceleration

For an object moving in a circle, there is an inward acceleration called centripetal acceleration, which is proportional to the square of the tangential speed and inversely proportional to the radius (a = v²/r). This acceleration is produced by a centripetal force that acts toward the center of the circular path, maintaining the object's circular motion.

Static Friction in Circular Motion

Static friction can provide the necessary centripetal force required for an object on a rotating platform to remain in circular motion. The frictional force, based on the coefficient of static friction and the normal force, must be equal to or greater than the centripetal force. This relationship helps determine the minimum coefficient of static friction needed to prevent the object from sliding off.

Transcript

Please give Ace some feedback