Lesson 8: Angular Kinematics and Centripetal Force

Question 1

What three quantities are we concerned with in angular kinematics?

Answer 1

angular displacement, angular velocity, and angular acceleration?

Question 2

What does angular displacement measure and what units do we use for angular displacement?

Answer 2

The angle through which a point or a line has been rotated, radians

Question 3

What is angular velocity and what units do we use for angular velocity?

Answer 3

The rate of change of angular displacement, rad/s

Question 4

What is angular acceleration and what units do we use for angular acceleration?

Answer 4

The rate of change of angular velocity, rad/s^2

Question 5

First angular kinematic equation

Answer 5

ωf = ωo + αt

Question 6

Second angular kinematic equation

Answer 6

ΔƟ = ωot + 1/2αt^2

Question 7

Third angular kinematic equation

Answer 7

ωf^2 = ωo^2 + 2αΔƟ

Question 8

Given arc length and distance of a point from the axis of rotation, how can you find the angular displacement?

Answer 8

ΔƟ = s/r

Question 9

Given tangential velocity and distance of a point from the axis of rotation, how can you find the angular velocity?

Answer 9

ω = v/r

Question 10

Given tangential acceleration and distance of a point from the axis of rotation, how can you find the angular acceleration?

Answer 10

α = a/r

Question 11

Two objects sit on a rotating platform. One object sits 1 m from the axis of rotation The second object sits 2 m from the axis of rotation. Which object has the larger tangential velocity?

Answer 11

object 2, r is larger
v =ωr

Question 12

Two objects sit on a rotating platform. One object sits 1 m from the axis of rotation The second object sits 2 m from the axis of rotation. Which object has the larger angular velocity?

Answer 12

both objects have the same angular velocity, they will both move through the same angle.

Question 13

Centripetal Acceleration

Answer 13

v^2/r

v is the velocity
r is the radius of the circular path

Question 14

True or false: an object moves around a curve at a constant speed. The object has no acceleration

Answer 14

False. speed is constant but direction changes, object experiences a centripetal acceleration

Question 15

Total acceleration

Answer 15

atotal= √(atangential^2 )+acentripetal^2

Question 16

Centripetal Force

Answer 16

Fc = (mv^2)/r

net force, equal to the sum of the forces that keep an object on a circular path

Question 17

A car drives around a circular unbanked curve. Draw a free body diagram for this situation. What force or forces are equal to the centripetal force?

Answer 17

Fc = (mv^2)/r = fs

Question 18

You are swinging an object in a vertical plane. Draw a free body diagram for the object at the bottom of the swing. What force or forces are equal to the centripetal force at this point?

Answer 18

Fc = (mv^2)/r = T - mg

Question 19

You are swinging an object in a horizontal plane above your head. Draw a free body diagram for this object. What force or forces are equal to the centripetal force?

Answer 19

Fc = (mv^2)/r = T

Question 20

What direction does the centripetal force always point in?

Answer 20

Centripetal force always points towards the center of the circular path.