M5 Topic 2 : Circular Motion

Question 1

what is the equation for an object instantaneous velocity of an object in circular motion

Answer 1

v=2πr/T

Question 2

what does each symbol mean for the instantaneous velocity of an object in circular motion, and what unit is it measured in

Answer 2

v= the instantaneous velocity of an object in circular motion (meters/second (m/s))
2πr= circumference of a circle (r= radius of circle)(metres (m))
T= the period (time for one revolution)(seconds (s))

Question 3

what is the equation for centripetal acceleration

Answer 3

a꜀ = v²/r

Question 4

what does each symbol mean in the centripetal acceleration equation and what unit is it measured in

Answer 4

a꜀= centripetal acceleration (ms⁻²)
v = instantaneous velocity (ms⁻¹)
r = the radius of the circle (metres (m))

Question 5

what is the angular velocity equation (2)

Answer 5

ω = Δθ/t
ω = v/r

Question 6

what does each symbol mean in the angular velocity equation (2 equations)

Answer 6

1.
ω = angular velocity (rad/s)
Δθ = change in angle (°)
t = time passed (seconds)

2.
ω = angular velocity (rad/s)
v = instantaneous velocity (m/s)
r = radius (metres)

Question 7

what is the equation for centripetal force

Answer 7

F꜀ = mv²/r

Question 8

what does each symbol mean in the centripetal force equation and what unit is it measured in

Answer 8

F꜀ = centripetal force (newtons)
m = mass of object in circular motion (kg)
v = instantaneous velocity of  object(m/s)
r = radius of object to centre of circle (metres)

Question 9

what changes in the centripetal force equation when applied to a banked track

Answer 9

F꜀ = friction + horizontal component of the normal force

Question 10

what is the design speed formula

Answer 10

√(rgtanθ)

Question 11

what does each symbol mean in the design speed formula and what unit is it measured in

Answer 11

r= radius of object on slope to the middle of the circle (metres(m))
g = gravitational acceleration constant (9.8 ms⁻²)
θ = angle the object is compared to the unbalanced force vector (°)

Question 12

what is the equation to calculate the centripetal force on a bank (ignoring friction)

Answer 12

F꜀ = mgtanθ

Question 13

what does each symbol mean in the centripetal force on a bank (ignoring friction) formula and what unit is it measured in

Answer 13

F꜀ =  centripetal force (newtons(N))
m = mass of the object (kg)
g = the gravitational acceleration constant (9.8 ms⁻²)
θ = angle the object is compared to the unbalanced force vector (°)

Question 14

In the vertical circular motion equation how is tension determined at the bottom of the circle

Answer 14

T = mv²/r + mg

Question 15

In the vertical circular motion equation how is tension determined at the top of the circle

Answer 15

T = mv²/r -mg

Question 16

In the vertical circular motion equation how is tension determined at the sides of the circle

Answer 16

T = mv²/r

Question 17

what does each symbol mean in the vertical circular motion equation sand what unit is it measured in

Answer 17

T = Tension (newtons (N))
v = instantaneous velocity of the object in vertical circular motion(ms⁻¹)
m = mass of object moving in vertical circular motion (kg)
r= radius of the circle (m)
g = the gravitational acceleration constant (9.8 ms⁻²)

Question 18

what is the equation for torque

Answer 18

t=r F sinθ

Question 19

what does each symbol mean in the Torque equation and what unit is each measured in

Answer 19

t = the torque (newton metres (Nm))
r = radius of the arm of the tool applying torque
F = the force applied to the tool handle
θ= the angle at which the force applied to the too; handle

Question 20

what is the right hand rule for torque (2)

Answer 20

(curled hand)

• curled fingers = the turning motion of the object ( applied force)
• thumb = direction of torque