Lesson 11 – Uniform Circular Motion

Minds-On

*this slide is not intended to be shown in class

Do the “Swing a plate with a cup of water over your head” demo. Ask students what keeps the water moving in a circle? If the plate broke free, where would the plate and water go?

Uniform Circular Motion◻Uniform Circular Motion is motion that occurs

when an object has constant speed and constant radius

◻ Imagine you have attached a rubber stopper to the end of a string and are whirling the stopper around your head in a horizontal circle

Centripetal Acceleration

◻An object in uniform circular motion is accelerating. Even though the speed is constant the vector direction of velocity is constantly changing.

◻This type of acceleration is referred to as Centripetal Acceleration.

Direction of Instantaneous Acceleration◻Instantaneous acceleration of uniform

circular motion is directed toward the centre of the circle

◻This can be illustrated by recalling the definition of instantaneous acceleration:

Direction of Instantaneous Acceleration

�⃑�= limΔ 𝑡→ 0

Δ �⃑�Δ𝑡If we only focus on the direction of we can see

that as , the vector starts approaching the vector and the vector points towards the center of the circle

Magnitude of Centripetal Acceleration

◻ The magnitude of centripetal acceleration is quantified by the following 3 equations:

Where:

is the magnitude of the centripetal acceleration (m/s2)

is the period (s)

is the speed (m/s)

is the radius (m)

is the frequency (Hz)

Example 1

The orbit of the Moon about the Earth is approximately circular, with a mean radius of 3.84 x 108 m. It takes 27.3 days for the moon to complete one revolution about the Earth.

a) Find the mean orbital speed of the Moon.

b) Its centripetal acceleration.

Example 2

David found that he can revolve a sling of length 0.600 m at the rate of 8.00 rev/s to hit Goliath. He then noticed that if he increased the length to 0.900 m, he could revolve the sling only 6.00 times per second.

a) Which rate of rotation gives the greater speed for the stone at the end of the sling?

b) What is the centripetal acceleration of the stone at 8.00 rev/s?

c) What is the centripetal acceleration at 6.00 rev/s?

Homework

Nelson Physics 12 (2001) Textbook page 127

Questions 3, 5, 7, 8