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In this lesson, we will learn how to use the angular speed equation of a body moving in a circular path.

Q1:

A wheel of radius 8 inches is rotating at a rate of . What is the linear speed in inches per second of the wheel, the angular speed in revolutions per minute, and the angular speed in radians per second? Give your answers correct to two decimal places if necessary.

Q2:

When burning data to a writable compact disc, the drive adjusts the angular speed in order to keep the linear speed constant where the data is being written. When writing along the outer edge of the disc, the angular speed of a drive is rpm (revolutions per minute). Find the linear speed if the CD has a diameter of 120 millimetres. Give your answers in millimeters per minute correct to two decimal places if necessary.

Q3:

A person is standing on the earth’s equator. Assuming the earth is a sphere with radius 3 9 6 0 miles, calculate their linear speed in miles per hour correct to two decimal places and their angular speed in radians per hour.

Q4:

A bicycle with 24-inch diameter wheels is traveling at 15 mph. Find the angular speed of the wheels in radians per minute (rad/min). How many revolutions per minute (rpm) do the wheels make? Give your answers correct to three decimal places if necessary.

Q5:

What is an angular speed of 18.4 rad/s in revolutions per hour? Give your answer correct to one decimal place.

Q6:

A wheel of radius 14 inches is rotating at a rate of 0 . 5 / r a d s . What is its linear speed in inches per second, its angular speed in revolutions per minute, and its angular speed in degrees per second? Give your answers correct to two decimal places where necessary.

Q7:

Find the speed of a particle which is moving on a circle of radius 35 m at an angular speed of 8.8 rad/s.

Q8:

A disc of radius 61 cm is spinning at 1 269 rpm. Find the speed of a particle on the outer rim, giving your answer in metres per second correct to one decimal place.

Q9:

Express, correct to one decimal place, an angular speed of 117 rpm in radians per second.

Q10:

A particle of mass 370 g describes complete vertical circles on the end of a light inextensible string of length 1 m. Given that the speed of the particle is 7 m/s at the highest point, find the tension 𝑇 in the string when the particle is at the lowest point of the circle. Give your answer to the nearest two decimal places. Take 𝑔 = 9 . 8 / m s 2 .

Q11:

A CD has diameter of 120 millimetres. When playing audio, a laser and photocell are used to scan data from tracks on the disc’s surface, starting near the centre and working outward. The angular speed of the disc is gradually reduced as this happens in order to keep the linear speed constant where the disc is being read. When reading along the outer edge of the disc, the angular speed is about 200 rpm (revolutions per minute). Find the linear speed in millimetres per minute, giving your answer correct to two decimal places if necessary.

Q12:

Amira and her sister were on a circular platform that was spinning around its centre at 12 revolutions per minute. Amira was 5 m from the centre of the platform and her sister was 3.5 m from the centre. Find the speeds and at which Amira and her sister, respectively, were moving. Give your answers in metres per second correct to one decimal place.

Q13:

A particle moves in a circular path of radius 6.1 m with an angular speed of 28 rpm. Find the speed of the particle to the nearest tenth of a metre per second.

Q14:

A disc of radius 12.5 cm spins at constant angular speed, taking 15 s to complete each revolution. What is the speed of the disc on its outer rim? Give your answer in metres per second correct to four decimal places.

Q15:

What is the angular speed 𝜔 of a particle that took 5 seconds to complete a circular path at a constant speed of 28 m/s? Give your answer correct to three decimal places, and use that value to determine the radius 𝑟 of the circular path correct to one decimal place.

Q16:

Express an angular speed of 68.1 rad/s in revolutions per minute. Give your answer correct to one decimal place.

Q17:

A race car is moving at 311 km/h round a circular track of radius 997 m. Determine, correct to three decimal places, its angular speed in radians per second.

Q18:

A truck with 32-inch diameter wheels is traveling at 60 mph. Find the angular speed of the wheels in radians per minute. How many revolutions per minute do the wheels make?

Q19:

A particle is moving in a horizontal circular path at a constant speed of 23 cm/s and a constant angular speed of 32 rpm. Find the radius of the path to the nearest hundredth of a centimetre.

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