1. Uniform Circular Motion
Practice Questions
Instructions:
Get a large whiteboard, markers, and towel(s)
Complete the practice problems in the time allotted (~3 minutes per question part)
Check your answer with the answer provided on screen
You will get a worksheet to work on for the remainder of the class period.

2. Practice Problem #1
A 27.5 kg child on a merry-go-round is moving with a speed of 1.35 m/s when sitting 1.20 m from the center of the ride.
Calculate the following:
(a) centripetal acceleration of the child
(b) the magnitude of the frictional force acting on the child (keep in mind the friction is the centripetal force)
(c) the coefficient of static friction between the child and the merry-go-round. We are assuming the child is not sliding.

3. Problem #1a--answer
A 27.5 kg child on a merry-go-round is moving with a speed of 1.35 m/s when sitting 1.20 m from the center of the ride. What is the centripetal acceleration of the child?
m = 27.5 kg
v = 1.35 m·s-1
r = 1.20 m
𝒂 𝒄 = 𝒗 𝟐 𝒓 = (𝟏.𝟑𝟓) 𝟐 𝟏.𝟐𝟎 =𝟏.𝟓𝟐 𝒎∙ 𝒔 −𝟐

4. Problem #1b--answer
A 27.5 kg child on a merry-go-round is moving with a speed of 1.35 m/s when sitting 1.20 m from the center of the ride. What is the force of friction acting on the child?
m = 27.5 kg
v = 1.35 m·s-1
r = 1.20 m
𝑭 𝒇 = 𝑭 𝒄 = 𝒎𝒗 𝟐 𝒓 = (𝟐𝟕.𝟓)(𝟏.𝟑𝟓) 𝟐 𝟏.𝟐𝟎
=𝟒𝟏.𝟖 𝑵

5. Problem #1c--answer
A 27.5 kg child on a merry-go-round is moving with a speed of 1.35 m/s when sitting 1.20 m from the center of the ride. What is the coefficient of static friction between the child and the ride?
m = 27.5 kg
v = 1.35 m·s-1
r = 1.20 m
Ff = 41.8 N
𝑭 𝒇 =𝝁 𝑭 𝑵 =𝝁(𝒎𝒈)
𝝁= 𝑭 𝒇 𝒎𝒈 = 𝟒𝟏.𝟖 (𝟐𝟕.𝟓)(𝟗.𝟖𝟏) =𝟎.𝟏𝟓𝟓

6. #2
A horizontal force of 280. N is exerted on a 2.00 kg discus as it is rotated uniformly in a horizontal circle (at arm’s length) at a radius of 1.00 m.
(a) What is its tangential speed?
(b) If it is released at an angle of 20.0°, and it hits a target that is at a vertical displacement of 0.00 m from the release point, how far downrange must the target be placed?

7. #3
A flat puck with a mass of kg is rotated in a circle at a speed of 2.25 m·s-1 on a frictionless air hockey tabletop. It is held in its circular path by a light cord which is connected to a dangling mass. If the radius of the circular path is m, what is the mass of the dangling mass?

8. #4
A kg ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.35 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 60.0 N, what is the maximum speed the ball can have?

9. #5
What is the coefficient of friction between the tires and the road if a car is to round a level curve of radius 85.0 m at a speed of 95 km·h-1 ?

10. #6
A ball on the end of a string is revolved at a uniform rate in a vertical circle of radius cm. Its speed is 4.15 m·s-1 and its mass is kg.
What is the tension in the string:
(a) at the top of the vertical circle
(b) at the bottom of the vertical circle