Circular Motion (DP IB Physics: HL)

A particle of mass m moves in a circle of radius r at uniform speed, taking time T for each revolution. What is the kinetic energy of the particle?

A 0.05 kg ball is attached to an inextensible string and whirled overhead such that it rotates in a horizontal circle.

What is the centripetal force on the ball if the string is 0.1 m long and the ball has a time period of  s?

A horizontal disc rotates uniformly at a constant angular velocity about a central axis normal to the plane of the disc.

Point X is on a distance 3L from the centre of the disc. Point Y is a distance L from the centre of the disc. Point Y has a linear speed v and a centripetal acceleration a.

What is the linear speed and centripetal acceleration of point X?

A girl of mass 50 kg is standing on a roundabout 100 cm from the centre. The force of friction on the girl is 600 N. What is the time period if the roundabout is rotating uniformly?

A spinning top makes twenty revolutions in five minutes in a clockwise direction.

What is the angular velocity of the spinning top?

A body moves in a circle with increasing angular velocity. At times t, the angles θ swept out by the body added cumulatively from the same reference point and its angular velocities ω are as follows:

The angular acceleration of the body:

A hammer thrower rotates a ball on a string in a circular path gradually increasing its angular velocity with each rotation. 

When the hammer releases the ball, the subsequent path taken by the ball is

An object at the end of a steel rod rotates in a vertical circle at a constant angular velocity. Which of the following statements correctly describes the tension in the rod?

For a particle moving in a circle with uniform speed, which of the following statements is incorrect?

A particle rotates clockwise in a horizontal circle of radius r with a constant angular velocity ω. The particle is at S at time zero and at P at time t. Q represents the projection of point P onto the diameter through S. Measured with respect to the centre of orbit O, the displacement, linear velocity and linear acceleration of Q along OS are x, v and a respectively. 

Which of the following sets of expressions is correct? 

		v	a
A.
B.
C.
D.

A simple pendulum consists of a bob of mass m at the end of a light inextensible thread of length d. The bob swings through point Y with velocity v and comes to an instantaneous rest at point X, where the string is just taut. 

What is the tension in the thread as the bob passes point Y? 

A particle travels in a circular path in a magnetic field with radius x and centripetal acceleration a. 

What is the time taken for 15 complete rotations? 

A mass m₁ is attached to one end of a light extensible string of length x. When the mass rotates with a linear speed v in a horizontal plane, an extension Δx is obtained. 

Which of the following shows the correct expression for another mass m₂, if it is attached to the same light extensible string and rotated with the same linear speed v but rotates at twice the radius as that produced by m₁?

Two bobs A and B, of equal mass, are connected by a light inextensible string of length l. 

Bob A is tied to a nail at the centre of a smooth table by another light, inextensible string of length 3l. The bobs are then set into uniform motion on the surface of the table with the same angular velocity. 

What is the ratio of the tension in the string connecting bob A and B to that in the string connecting bob A to the nail? 

An aircraft moves in a horizontal plane at a constant linear speed v and makes a turn of radius r. 

Which of the following expressions is true for the tilt angle θ?

You may wish to use the relationship:

The maximum speed for a car to safely move round a corner when the road is dry is 10 m s^–1. The maximum frictional force between the road surface and the wheels of the car is halved when the road is wet. 

What is the maximum safe speed for a car to go round the corner when the road is wet? 

A conker attached to a string is whirled in a vertical circle at constant speed. 

Which of the following correctly shows the variation of the tension T in the string with the angular displacement θ? 

A small object is attached to a string and whirled in a vertical circle at a constant speed. The magnitude of the net force F on the object at the top of the circle is given by:

Where T is the tension in the string, m is the object's mass and g is the acceleration of free fall.

The magnitude of the net force on the object at the bottom of the circle is given by: 

Which of the following statements is correct?

Two masses m₁ and m₂ are fixed on a horizontal circular rotating platform. m₂ is half as massive as m₁ and is fixed at a distance three times as far from the centre as m₁. The net force on m₁ is F₁ and the net force on m₂ is F₂.

Which of the following statements is correct?