P.3.6.1.1 Circular motion

An object of mass m moves in a circle of radius r. It completes n revolutions every second.

What is the kinetic energy of the object?

• 
• 
• 2mπ²n²r²

• 4mπ²n²r²

A planet of mass M and radius R rotates so quickly that material at its equator only just remains on its surface.

What is the period of rotation of the planet?

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• 
• 
• 

A bob of mass 0.50 kg is suspended from the end of a piece of string 0.45 m long. The bob is rotated in a vertical circle at a constant rate of 120 revolutions per minute.

What is the tension in the string when the bob is at the bottom of the circle?

• 5.8 N

• 31 N

• 36 N

• 40 N

A helicopter circles continuously at a constant speed around a horizontal path of diameter 800 m, taking 5.0 minutes to complete each orbit of the path.

What are the speed v and the centripetal acceleration a of the helicopter?

• A

• B

• C

• D

A string passes through a smooth thin tube. Masses m and M are attached to the ends of the string. The tube is moved so that the mass m travels in a horizontal circle of constant radius r and at constant speed v.

Which of the following expressions is equal to M ?

• 
• mv²rg

• 
• 

What is the angular speed of a car wheel of diameter 0.400 m when the speed of the car is 108 km h⁻¹?

• 75 rad s⁻¹

• 150 rad s⁻¹

• 270 rad s⁻¹

• 540 rad s⁻¹

A ball of mass 0.30 kg is attached to a string and moves in a vertical circle of radius 0.60 m at a constant speed of 5.0 m s–1.

Which line, A to D, in the table gives the correct values of the minimum and maximum tension in the string?

• A

• B

• C

• D

A satellite X is in a circular orbit of radius r about the centre of a spherical planet of mass M.

Which line, A to D, in the table gives correct expressions for the centripetal acceleration a and the speed v of the satellite?

• A

• B

• C

• D

A small mass is placed at P on a horizontal disc which has its centre at O. The disc rotates anti-clockwise about a vertical axis through O with constant angular speed.

Which one of the following describes the force which keeps the mass at rest relative to the disc when in the position shown?

• the weight of the mass

• a frictional force from P to Q

• a frictional force directed away from O

• a frictional force directed towards O

A 0.20 kg mass is whirled round in a vertical circle on the end of a light string of length 0.90 m.

At the top point of the circle the speed of the mass is 8.2 m s^–1. What is the tension in the string at this point?

• 10 N

• 13 N

• 17 N

• 20 N