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physics Physics For High Schools (KS4)
 
Solved problems for the chapter:
 

Angular and Linear Speed

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Circular Motion for KS4
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Detailed solution steps are available at:
 
https://en.openprof.com/wb/chapter:angular_and_linear_speed/4976/


Example 1.

A car engine rotates at 2400 rpm. What is the angular frequency of the engine in Hz?

    
Example 2.

A body moves in a circular path with a radius of 0.4 m. The time taken for one rotation is 2 s. What is the linear speed of the body?

    
3.

What is the linear speed of the Earth's orbit around the Sun if the average distance of the Earth from the Sun is 150 million kilometres and the Earth orbits the Sun in 365 days?

    
4.

Children run uniformly at a speed of 4 round a circle of radius 40 m. What is the frequency of their rotation?

    
5.

An athlete runs uniformly on a circular track with a radius of 60 m. After 20 s, the angular displacement is . How fast did he run?


    
6.

A plane is approaching an airport at a speed of 360 . The controller informs the pilot to make another lap around the airport before landing so that he will land in 3 minutes. What radius of rotation will the pilot choose?

    
7.

What is the speed at which the tip of the hour hand of a clock is moving if the length of the hand is 2 cm?

    
8.

Two bodies rotate on a horizontal plate with frequency . The radius of rotation of the first body is three times that of the second body. What is the relationship between their linear speeds?


    

9.

A plate makes 3 revolutions in 2 s. What is the length of an arc that is described by a point located at a distance of 4 cm from the centre of rotation of the plate in 1 s?

    
10.

What is the ratio of the frequency of the minute hand to that of the hour hand on the clock?

    
11.

The moon orbits the Earth in 27.3 days. How far in its orbit does it travel in 24 hours? The distance of the Moon from the Earth is 384000 km.

    
12.

A gear is a toothed wheel which, by means of teeth on the circumference, drives another toothed wheel.


We have two gears. The larger gear has 34 teeth and the smaller has 15 teeth. The gears are connected as shown in the figure. The larger gear rotates at a frequency of 2 Hz. With what frequency does the smaller gear rotate?


Gears

    
13.

A body rotates uniformly at an angular displacement of in 0.1 s. What is the frequency of rotation of the body?


Angular displacement

    
14.

Two runners start running at the same time from the same position on a track in opposite directions. The running track is circular in shape with a radius of 64 m. They move uniformly and the speed of the first and the second runner are 8 and 6 respectively. How long will it take for them to meet?

    
15.

What time is it in Tokyo if it is exactly noon in Ljubljana? Tokyo lies at longitude East and Ljubljana at longitude East.

    
16.

A body moves in a circle of radius 60 cm at a constant speed of around the circle. What is the arc length described by the body in 30 s? How long does it take to rotate 20 times round the circle?

    
17.

A wheel with a radius of 60 cm rotates evenly, making 4 revolutions in 6 seconds. What is the tangential speed of the wheel? What is the arc length described by the wheel in 20 s?

    
18.

How many revolutions per minute can the rotor of a helicopter make so that the speed of the edge of the rotor blades is less than the speed of sound (340 ) if the length of the blades is 6 m?

    

19.

At 12 o'clock, the hour and minute hands of a clock overlap each other. At what time will they overlap again?

    
20.

An electric motor rotates at a frequency of 600 revolutions per minute. A wheel with a radius of 10 cm is attached to the axis of the electric motor. The wheel is connected to another wheel with a radius of 40 cm via a belt (see the figure below). What is the speed of the belt and at what frequency does the larger wheel rotate?



Pulley

    
21.

An object attached to a 0.6 m string is rotated in a vertical plane such that it makes 2 rotations per second. The moment it is directed vertically upwards, the string breaks. How high will it fly?

    
22.

The Moon orbits the Earth at a distance of 384,000 km. It completes a circular arc of 88,400 km in 24 hours. It orbits in the same direction as the Earth rotates and rises at 6 p.m. on an observed day. When will it rise the next day?

    
23.

A load is lifted using a fixed and movable pulley, as shown in the figure. The radius of the wheel of both pulleys is 4 cm. On the side of the attached pulley, the rope is pulled at a speed of 2 dm/s. At what speed is the load lifted? What are the rotational frequencies of both wheels?


The load is hung on the left pulley

    
24.

A body rotates round a circle of radius r. After 1.4 s, the body has described an arc length of 80 cm along the circle and an angle of at the centre of the circle. What is the angular velocity and radius of rotation of the circle?

    
25.

The minute hand on a clock is 20% longer than the hour hand. Determine the ratio of the tangential velocities of the tips of the minute hand to that of the hour hand.

    
26.

A clock is 2 minutes behind each day. What is the ratio of the frequency of rotation of the hands of this clock to that which shows the exact time?

    
27.

A disc-shaped grinding stone with a radius of 12 cm is attached to a stand 60 cm high and rotates in a horizontal plane with a frequency of 16 Hz. What is the velocity of the particle located on the circumference of the disk? At some point, the particle on the perimeter peels off. At what speed and in which direction is it flying? How far does it fall before hitting the ground?

    
28.

How long does it take a pendulum to move from one extreme position to another if it oscillates at a frequency of 4.4 Hz?