What is the relationship between angular velocity (ω) and linear velocity (v) for an object moving in a circle of radius r?

A. v = ω/r

B. v = ω * r

C. v = r/ω

D. v = ω^2 * r

Which force is responsible for keeping an object moving in a circular path?

A. Gravitational force

B. Centripetal force

C. Frictional force

D. Normal force

A car is moving on a flat curve at a constant speed. Which of the following forces provides the necessary centripetal force?

A. Gravitational force

B. Normal force

C. Frictional force

D. Air resistance

What is the direction of centripetal acceleration for an object moving in a circular path?

A. Tangential to the circle

B. Opposite to the direction of motion

C. Outwards from the centre of the circle

D. Towards the centre of the circle

In a banked curve, which component of the weight of the vehicle provides the necessary centripetal force?

A. Component parallel to the surface of the road

B. Component perpendicular to the surface of the road

C. The entire weight of the vehicle

D. None of the above

a) A car is moving in a circular path of radius 50 m with a constant speed of 20 m/s. Calculate the angular velocity of the car. [2]

b) If the car completes 5 revolutions, determine the total distance travelled by the car. [2]

a) Define the term 'centripetal acceleration'. [1]

b) A cyclist is moving in a circular track of radius of 100 m with a speed of 15 m/s. Calculate the centripetal acceleration of the cyclist. [3]

a) A stone is tied to a string and is being whirled in a vertical circle. What is the minimum speed the stone should have at the topmost point to complete the circle? [2]

b) If the length of the string is 1.5 m and the stone has a speed of 5 m/s at the bottommost point, calculate the tension in the string at that point. Assume the mass of the stone is 0.5 kg. [2]

a) A car is moving in a circular path of radius 50 m with a constant speed of 20 m/s. Calculate the centripetal force acting on the car if its mass is 1000 kg. [3]

b) If the radius of the circular path is doubled while keeping the speed constant, how will the centripetal force change? [2]

c) Explain the direction of the centripetal force acting on the car while it is in circular motion. [2]

a) A satellite is moving in a geostationary orbit around the Earth. Explain the significance of a geostationary orbit. [2]

b) If the gravitational force provides the necessary centripetal force for the satellite's motion, derive the expression for the speed of the satellite in terms of the gravitational constant (G), mass of the Earth (M), and the radius of the orbit (r). [3]

c) Discuss the applications of satellites in geostationary orbits. [2]