TUTORIAL PHYSICS DP014

CHAPTER 6: CIRCULAR MOTION SESSION 2021/2022

N, what is the maximum speed the ball can have?

7. A device for training astronauts and jet fighter pilots is designed to rotate a trainee in a
horizontal circle of radius 12.0 m. If the force felt by the trainee on her back is 7.85 times
her own weight, how fast is she rotating? Express your answer in both m s-1 and rev s-1.

8. (a) Define centripetal acceleration and centripetal force.

(b) A cyclist is moving at the speed of 4.9 m s-1 in a circle of radius 10 m. calculate the
smallest value of the coefficient of friction between the tyres and the ground for the
cylist to remain in balance.

9. A 1500 kg car is moving on a flat horizontal curved road. If the radius of the curve is 350
cm and the coefficient of static friction between the tyres and dry road, µs = 0.5;
a. calculate the maximum speed the car can have and still make the turn successfully.
b. suppose the car travels on this curve on a wet day and begins to skid when its speed
reaches 8 m s-1. Calculate the coefficient of static friction, µs in this case.

10. A car is safely negotiating an unbanked circular turn at a speed of 25 m s -1. The road is
dry, and the maximum static frictional force acts on the tyres. Suddenly a long wet patch
in the road decreases the maximum static frictional force to one-third if its dry road value.
If the car is to continue safely around the curve, what speed must be driver slow the car?

11. A car is traveling in uniform circular motion on the road, whose radius is r. The road is
slippery, and the car is just on the verge of sliding.
a. If the car’s speed were doubled, what would be the smallest radius at which the car
does not slide? Express your answer your in terms of r.
b. What would be your answer to part (a) if the car were replaced by the one weighed
twice as much and the car’s speed still being doubled?

29

CHAPTER 7: ROTATIONAL OF RIGID BODY SESSION 20212022

CHAPTER 7: ROTATIONAL OF RIGID BODY

7.1 Rotational Kinematics

a) Define:
i) Angular displacement ( )

ii) Average angular velocity (av )
iii) Instantaneous angular velocity ( )

iv) Average angular acceleration (av )

v) Instantaneous angular acceleration ( )

b) Use:

i) Angular displacement ( )

ii) Average angular velocity (av )
iii) Instantaneous angular velocity ( )

iv) Average angular acceleration (av )
v) Instantaneous angular acceleration ( )

c) State parameters in rotational motion with their corresponding quantities in linear motion.

d) Use parameters in rotational motion with their corresponding quantities in linear motion:

s = r , v = r, at = r, ac = r2 = v2
r

e) Solve problem related to rotational motion with constant angular acceleration.

 =  +  t, =  t + 1t2 and 2 = 2 + 2
2

30

CHAPTER 7: ROTATIONAL OF RIGID BODY SESSION 20212022

OBJECTIVE QUESTION

1. An angular speed of 25 rotations per minute is equivalent to

A. 0.42 rad s-1 C. 238 rad s-1

B. 2.62 rad s-1 D. 420 rad s-1

2. The rate of rotation of a wheel is increased uniformly from 2 rad s-1 to 5 rad s-1 in 6 s. The
angular displacement of the rotated wheel is

A. 21 rad C. 42 rad
B. 40 rad D. 60 rad

3. The angular velocity of a wheel increases uniformly from 3.6 rad s-1 to 6.0 rad s-1 in 3.0

s. What is the average angular velocity?

A. 0.8 rad s-1 C. 2.8 rad s-1

B. 2.4 rad s-1 D. 4.8 rad s-1

4. A wheel rotating at 2.0 revolutions per second slows down uniformly. It stops after 5.0

s. What is its angular retardation?

A. 0.40 rad s-2 C. 2.51 rad s-2

B. 1.25 rad s-2 D. 5.02 rad s-2

5. A disc of radius 0.45 m rotates at a constant rate of 5.0 revolutions per second. What are
the tangential and radial accelerations of a point on the rim of the disc?

Tangential acceleration Radial acceleration
444 m s -2
A. 0
B. 444 m s -2 0
C. 11.3 m s -2 444 m s -2
D. 444 m s -2 11.3 m s-2

31

CHAPTER 7: ROTATIONAL OF RIGID BODY SESSION 20212022

STRUCTURED QUESTIONS

1. A bicycle wheel rotates with an angular velocity of 10π rad s-1. At 3 seconds after that,
its angular velocity becomes 4π rad s-1. Calculate
(a) the angular acceleration of the wheel
(b) the angular displacement at 3 seconds.

2. A windmill rotates at a constant speed and takes 30.0 s to complete one revolution.
(a) Determine the angular velocity of the windmill in rad s-1.
(b) Calculate the time taken by the windmill to rotate through an angle of 120.

3. A wheel turns about its axis of rotation at uniform angular acceleration from rest to reach
an angular velocity of 30 rad s-1 in 20 s. Calculate;
(a) Its angular displacement.
(b) Its tangential acceleration at point

4. A spinning top has an initial angular velocity of 600 rpm. The velocity then decreases at
a constant retardation to 300 rpm. in 6.0 s. Determine the
(a) initial and final angular velocity in rad s−1
(b) angular acceleration,
(c) number of revolutions the body has turned through during the 6.0 s interval,
(d) extra time needed by the body to come to a stop if it continues to slow down at the
same rate.

5. A rigid body rotates about a fixed axis through a point in the body, with uniform angular
velocity of 600 r.p.m. The velocity then decreases at a constant retardation to 300 r.p.m.
in 6.0 s. Determine:
(a) the angular acceleration,
(b) the number of revolutions the body has turned through in the 6.0 s.
(c) the extra time needed by the body to come to a stop if it continues to slow down
at the same rate.

32

CHAPTER 8: HEAT, GAS LAW AND THERMODYNAMICS SESSION 20212022

CHAPTER 8: HEAT, GAS LAW AND THERMODYNAMICS

8.1 Heat

a) Define heat conduction.

b) Solve problems related to rate of heat transfer , dQ = −kA dT  through a cross-sectional area
dt dx 

*only one material

c) Discuss graphs of temperature – distance, T-x for heat conduction through insulated.
*one material & lagged material

8.2 Ideal Gas Equations

a) State Gas’s Law
b) Sketch the following graphs of an ideal gas:

i) p – V graph at constant temperature.
ii) V – T graph at constant pressure.
iii) p – T graph at constant volume.
c) Explain the following graphs of an ideal gas:
i) p – V graph at constant temperature.
ii) V – T graph at constant pressure.
iii) p – T graph at constant volume.
d) State ideal gas equation
e) Use ideal gas equation, pV = Nrt

8.3 Thermodynamics

a) State the first law of thermodynamics.
b) Solve problem related to first law of thermodynamics.
c) Define the thermodynamics process

(i) Isothermal
(ii) Isochoric
(iii) Isobaric
(iv) Adiabatic
d) Interpret p-V graph for all the thermodynamics processes.
(Experiment 6: Heat)

33

CHAPTER 8: HEAT, GAS LAW AND THERMODYNAMICS SESSION 20212022

OBJECTIVE QUESTIONS

1. Which of the following statements best represents the characteristic of heat as a form of
energy?
A. Heat needs a medium
B. The magnitude of heat depends on its density
C. Heat is transferred from a point or region to another
D. Heat is transferred from a high pressure region to low pressure region

2. Which of the following graph DOES NOT obey the ideal gas law?

A. P C. P
T constant V constant

V T
V P constant
B. P D.

T constant

VT

3. An ideal gas is cooled at constant volume, then expanded at constant pressure and finally
compressed isothermally until it returned to its original state. Which of the following graphs
represents all these processes?

A. B.
p p

C. V V
p D. V

p

V
34

CHAPTER 8: HEAT, GAS LAW AND THERMODYNAMICS SESSION 20212022

4. Which of the following statements is TRUE concerning an adiabatic process for a
thermodynamics system?
A. No change in the kinetic energy of the gas molecules
B. No change in the internal energy of the system
C. No temperature increase of the gas
D. No heat transfer into or out of the system

STRUCTURED QUESTIONS

1. Define heat and state its SI unit.

2. (a) Define thermal conductivity.

(b) An aluminum rod has a diameter of 3 cm and thickness of 0.6 m. One end of the
rod is placed in boiling water and the other end in ice. Calculate the quantity of heat
transferred through the rod within 1 minute.
(kaluminium = 205 W m-1 K-1)

(c) On the same axes, sketch the temperature versus length graph for an insulated
conductor.

3. (a) A Styrofoam box used to keep drinks cold at a picnic has total wall area of
0.80 m2 and wall thickness is 2.0 cm. It is filled with ice, water and cans at 0C.
What is the rate of heat flow into the box if the temperature of outside wall is 30
C?
(kstyrofoam = 0.01 W m-1 K-1)

(b) The rate of heat conduction is 80 kJ per hour at a thin wall with an area of 14 cm2.
If the temperature gradient across the wall is 15C m-1, calculate the thermal
conductivity, k

4 (a) State Boyle’s Law and Charles’s Law.

(b) A vessel of volume 45 liters contains 3.0 moles of gas at 35 ºC. Calculate the gas
pressure.

5. State first law of thermodynamics.

6. Define the following thermodynamics processes:
(i) isothermal
(ii) isovolumetric
(iii) isobaric
(iv) adiabatic

35

CHAPTER 8: HEAT, GAS LAW AND THERMODYNAMICS SESSION 20212022

7. Sketch p-V graph for all the thermodynamic processes in the same axes.
(i) isothermal
(ii) isovolumetric
(iii) isobaric
(iv) adiabatic

8. In each of the following situations, find the change in internal energy of the system.
(a) A system absorbs 2090 J of heat and at the same time does 400 J of work.
(b) A system absorbs 1255 J of heat and at the same time 420 J of work is done on it.
(c) 5020 J is removed from a gas held at constant volume. Give your answer in
kilojoules.

9. As an ideal gas is compressed isothermally, the compressing agent does 36 J of work. How
much heat flows from the gas during the compression process?

10. (a) A gas undergoes the following thermodynamic processes: isobaric expansion,
heated at constant volume, compressed isothermally and finally expands
adiabatically back to its initial pressure and volume. Sketch all processed given
on the same P- V graph.

(b) A gas of volume 0.02m3 at a pressure of 2.0 × 105 Pa undergoes an isothermal
compression. If the final pressure is 4.0×105 Pa, what is its volume?

(c) Sketch the pressure-volume graph for an isothermal compression.

36

KELANTAN MATRICULATION COLLEGE

PHYSICS UNIT