Rotational Motion - Definitions

Question 1

What is Velocity (Rotational Motion)

Answer 1

The rate of change of displacement.

Question 2

What is Acceleration (Rotational Motion)

Answer 2

The rate of change of velocity.

Question 3

What is Moment of Inertia (Rotational Motion)

Answer 3

A measure of an object’s resistance to angular acceleration about a given axis.

Question 4

What is The Principle of Conservation of Angular Momentum (Rotational Motion)

Answer 4

The total angular momentum before an interaction is equal to the total angular momentum after the interaction, provided there are no external torques acting on the objects.

Question 5

Derive v = u + at (Rotational Motion)

Answer 5

begin with a = d^2s/dt^2

integrate w.r.t time

(Z) d^2s/dt^2 dt = (Z) a dt

ds/dt = at + k

t= 0: ds/dt = u so k = u

t = t: ds/dt = v

v= u + at

Question 6

Derive s = ut + 1/2 at^2 (Rotational Motion)

Answer 6

begin with v = ds/dt = u + at

integrate w.r.t time

(Z) ds/dt x dt = (Z) u + at x dt

s = ut + 1/2 at^2 + k

t = 0; s = 0; k = 0;

s = ut + 1/2 at^2

Question 7

Derive v^2 = u^2 + 2as (Rotational Motion)

Answer 7

start with v = u + at

v^2 = (u + at)^2 = (u + at)(u+at)

v^2 = u^2 + 2a (ut + 1/2 at^2)

v^2 = u^2 + 2as

Question 8

What does the gradient of a curve (or straight line) on a displacement-time graph give? (Rotational Motion)

Answer 8

The instantaneous velocity

Question 9

What does the gradient of a curve (or straight line) on a velocity-time graph give? (Rotational Motion)

Answer 9

The instantaneous acceleration

Question 10

What is one full revolution of 360 degrees equal to in radians? (Rotational Motion)

Answer 10

2(pi) radians

Question 11

What is 1 radian equal to in degrees? (Rotational Motion)

Answer 11

57.3 degrees

Question 12

What is angular velocity of a rotating object, w? (Rotational Motion)

Answer 12

The rate of change of angular displacement

Question 13

What is the angular acceleration of a rotating object, a? (Rotational Motion)

Answer 13

The rate of change of angular velocity.

Question 14

What happens to an object moving in a circular path? (Rotational Motion)

Answer 14

It has a changing velocity and is therefore accelerating

• because velocity is vector quantity and direction of travel is constantly changing.

Question 15

What is the tangential acceleration of a rotating object, at? (Rotational Motion)

Answer 15

The rate of change of linear velocity.

Question 16

What is tangential acceleration measured in? (Rotational Motion)

Answer 16

Metres per second squared (ms-2)

Question 17

What is meant by centripetal acceleration? (Rotational Motion)

Answer 17

The acceleration of an object moving in a circular path which acts towards the centre of axis in rotation.

Question 18

Centripetal Force example in a vehicle (Rotational Motion)

Answer 18

• When a vehicle is turning a corner at speed, you may slide along the chair
• Because friction between you and seat is insufficient to provide central force
• Instead of being thrown outwards, you are in reality continuing in straight line while car moves inwards.

Question 19

If an object has a centripetal acceleration, what type of force will be acting on it. (Rotational Motion)

Answer 19

Unbalanced force

(Centripetal force, always acting towards centre of the circle).

Question 20

Centripetal force in aeroplane banking at an angle (Rotational Motion)

Answer 20

• When it banks, lift provided by the wings is at an angle.
• Provides upwards component to balance the weight
• Centripetal component to cause the plane to turn

Question 21

Centripetal force in a conical pendulum (Rotational Motion)

Answer 21

• There must be a centripetal force responsible for maintaining path
• Force comes from horizontal component of the tension in string.

Question 22

What is torque? (Rotational Motion)

Answer 22

A force which produces rotation about an axis.

Question 23

What is a common example of the application of torque?. (Rotational Motion)

Answer 23

When a spanner is used to tighten or loosen a nut.

Question 24

What does an unbalanced torque cause a change in? (Rotational Motion)

Answer 24

The angular motion of an object.

Question 25

What is angular momentum, L, measured in? (Rotational Motion)

Answer 25

Kilogram metres squared per second (kgm^2 s -1)

Question 26

What is moment of inertia measured in? (Rotational Motion)

Answer 26

Kilogram metres squared (kgm^2)

Question 27

What is angular velocity measured in? (Rotational Motion)

Answer 27

radians per second (rad s-1)

Question 28

What is the principle of conservation of linear acceleration? (Rotational Motion)

Answer 28

The total momentum before an interaction is equal to the total momentum after the interaction, provided there are no external forces acting on the objects.

Question 29

The spinning ice skater ice skater example (Angular momentum)

(L = Iw)

(Rotational Motion)

Answer 29

• Skater will have a certain angular momentum with arms extended
• If he pulls his arms in towards his body his angular momentum must remain constant.
• Since moment of inertia has decreased, angular velocity increases and he therefore spins faster.

Question 30

What happens when torque does not work on a body to make it rotate? (Rotational Motion)

Answer 30

It gains kinetic energy