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]

Which of the following is a fictitious force experienced by an observer in a rotating frame of reference?

A. Centripetal force

B. Gravitational force

C. Centrifugal force

D. Frictional force

For an object to complete vertical circular motion, the minimum speed at the topmost point must be:

A. Equal to the square root of the gravitational acceleration

B. Equal to the gravitational acceleration

C. Equal to the square root of 5 times the gravitational acceleration

D. Equal to 5 times the gravitational acceleration

Which of the following applications involves the principle of circular motion?

A. A pendulum clock

B. A satellite orbiting the Earth

C. A ball thrown upwards

D. A car moving on a straight road

If the radius of a circular path is doubled while keeping the speed constant, the centripetal force required to keep the object in motion will:

A. Remain the same

B. Double

C. Halve

D. Quadruple

In the context of circular motion, what does the period represent?

A. The time taken for one complete revolution

B. The distance covered in one revolution

C. The speed of the object

D. The acceleration of the object

a) Define angular velocity and differentiate it from linear velocity. [2]

b) A child is sitting on the edge of a merry-go-round that is turning with an angular velocity of 2 rad/s. If the radius of the merry-go-round is 3 meters, calculate the child's linear velocity. [3]

c) Discuss the relationship between linear velocity and the radius of a circular path for a constant angular velocity. [2]

a) What is the significance of the centripetal force in maintaining an object in circular motion? [2]

b) A stone is tied to a string and whirled in a vertical circle of radius 1.5 meters. If the tension in the string at the topmost point is half of that at the bottommost point, calculate the speed of the stone at the topmost and bottommost points. Assume the acceleration due to gravity to be 9.81 m/s^2. [4]

c) Discuss the conditions necessary for an object to complete vertical circular motion. [2]

a) Define the term 'centripetal acceleration' and explain its significance in circular motion. [2]

b) A motorbike is moving on a circular track of radius 100 m with a speed of 25 m/s. Calculate its centripetal acceleration. [2]

c) If the motorbike increases its speed such that the centripetal acceleration doubles, what would be its new speed? [3]

d) Discuss the effect on the centripetal acceleration if the radius of the circular track is halved while keeping the speed constant. [2]

a) Describe the concept of 'banking' with respect to circular motion. [2]

b) A car is moving on a banked road of angle 30 degrees with a speed of 20 m/s without the assistance of friction. Calculate the radius of the circular path for which the banking angle is most appropriate. [3]

c) Explain the role of friction in assisting cars to move on banked roads. [2]

d) Discuss the implications if the car exceeds the optimal speed for the given banking angle. [2]

a) Differentiate between 'angular velocity' and 'frequency' in the context of circular motion. [2]

b) A Ferris wheel completes 3 revolutions in 2 minutes. Calculate its angular velocity in rad/s. [3]

c) If a person is sitting 15 m from the centre of the Ferris wheel, what is their linear speed? [2]

d) Discuss the relationship between the linear speed of a point on a rotating object and its distance from the centre of rotation. [2]