Motion in a Circle

Question 1

How does a perpendicular force affect an object?

Answer 1

A perpendicular force changes the body’s direction of motion.

Question 2

Definition of the angle of a sector

Answer 2

The angle of a sector is the ratio of arc length and the radius of the circle.

Question 3

Formula for arc sector

Answer 3

s = rθ, 2π rad
s is arc length, r is radius

Question 4

Definition of the radian

Answer 4

One radian is the angle subtended at the centre of the circle when the arc length is the same as the radius of the arc.

Question 5

Definition of angular displacement θ

Answer 5

Angular displacement θ is defined as the angle swept by an object moving along an arc about an axis from its angular position to its final angular position. (2π rad)

Question 6

Definition of angular velocity ω

Answer 6

Angular velocity ω of an object is defined as the rate of change of angular displacement.

Question 7

What is to note about the linear velocity in a circular path?

Answer 7

The direction of instantaneous linear velocity of a body which is moving in a circular path is always tangential to the circular path at that point.

Question 7

SI unit for angular displacement and angular velocity

Answer 7

Angular displacement: radians
Angular velocity : rad s^-1

Question 8

Formula for angular velocity ω

Answer 8

ω = dθ/dt

Question 9

What is the magnitude of linear velocity(circular path)?

Answer 9

v = ds/dt
v = d(rθ) /dt
v = r dθ/dt
v = rω

Question 10

What is the definition of period in a circular motion?

Answer 10

Period T in a circular motion is defined as the time taken to complete one revolution.

Question 11

Formula for period T(circular path)?

Answer 11

T = 2π /ω

Question 12

Definition of frequency(circular motion)

Answer 12

The frequency f of a circular motion is teh number of revolutions the object makes per unit time.

Question 13

Formula for frequency(circular path)
SI unit and base unit

Answer 13

f = ω/ 2π
Hertz(Hz), s^-1

Question 14

At constant angular velocity, what happens to the kinetic energy and the linear momentum?

Answer 14

The kinetic energy is constant but the linear momentum varies.

Question 15

Definition of centripetal force

Answer 15

Centripetal force is the resultant/net force acting on an object moving in an uniform circular motion.

Question 16

What is the centripetal acceleration in a circular path?

Answer 16

The acceleration that is perpendicular to the direction of motion because there is no acceleration along the direction of motion(Ke is the same)

Question 17

In uniform circular motion, what happens to linear velocity, angular velocity and centripetal acceleration?

Answer 17

Linear velocity varies.
Angular velocity is constant.
Centripetal acceleration is varying.

Question 18

How to find magnitude of centripetal acceleration?(ac)

Answer 18

ac = v^2/r or a = rω^2

Question 19

How to find magnitude of centripetal force?

Answer 19

F = mac or F = Mrω^2 or F = mv^2/r

Question 20

For a uniform horizontal circular motion , what happens?

Answer 20

The linear speed and angular speed remains constant.
Centripetal force acts horizontally towards the centre of the circle.
Fy = 0

Question 21

For a uniform vertical circular motion , what happens?

Answer 21

The linear speed and angular speed remains constant.
Cnetripetal force acts towards the centre of the circle.
For an object to remain in contact, N>0
Fy = Fnet = mv^2/r

Question 22

For a non-uniform vertical circular motion , what happens?

Answer 22

The magnitude of linear speed changes.
Apply conservation of energy to find speed at any point of motion.