Circular Motion Exercise 1

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Questions and Answers

A particle is moving on a circular path of radius 0.5 m at a constant speed of 10 ms⁻¹. Find the time taken to complete 20 revolutions.

6.28 s

What are the angular velocities of the hour-hand and minute-hand of a clock?

1.45 x 10⁻⁴ rad s⁻¹, 1.75 x 10⁻³ rad s⁻¹

The speed of an object in uniform circular motion is 6.0 ms⁻¹, the diameter of the circle is 2.5 m. What is the angular velocity?

4.8 rad s⁻¹

A particle moving in a circle takes 0.25 s to complete one revolution. How many complete revolutions per minute (rpm) does the particle perform?

240 rpm Signup and view all the answers

A particle in uniform circular motion takes 3.0 s to move from one end A of a diameter to the other end B. The diameter of the circle is 5.00 cm. Calculate the angular velocity and the speed.

1.05 rad s⁻¹, 2.62 x 10⁻² ms⁻¹ Signup and view all the answers

An object is moving in a circle of radius 40 cm with constant angular velocity of 6 rads⁻¹. Find the velocity of the object and the time for one complete revolution.

2.4 ms⁻¹, 1.05 s Signup and view all the answers

A 200 g mass is moving with uniform angular velocity in a circle of radius 80 cm on a smooth horizontal surface. If the mass completed 10 revolutions in one second, calculate the angular velocity and the linear velocity.

62.8 rad s⁻¹, 50.3 ms⁻¹ Signup and view all the answers

If a disc 30 cm in diameter rolls 65 m along a straight line without slipping, calculate the number of revolutions it would make in the process and the angular displacement it would go through by a speck of gum on its rim.

69 rev, 138π rad Signup and view all the answers

During a certain period of time, the angular displacement of a swinging door is described by θ = 5.00 + 10.0t + 2.00t² where θ is radians and t is in seconds. Determine the angular displacement, angular speed and angular acceleration at time t = 0 s and at time t = 3.00 s.

5.00 rad, 10.0 rad s⁻¹, 4.00 rad s⁻², 53.0 rad, 22.0 rad s⁻¹, 4.00 rad s⁻² Signup and view all the answers

A disk 8.00 cm in radius rotates at a constant rate of 1200 rev min⁻¹ about its central axis. Determine the angular speed, the tangential speed at a point 3.00 cm from its centre, the radial (centripetal) acceleration of a point on the rim and the total distance a point on the rim moves in 2.00 s.

125.6 rad s⁻¹, 3.77 ms⁻¹, 11.8 ms⁻², 15.08 m Signup and view all the answers

A 0.35 m diameter grinding wheel rotates at 2500 rpm. Calculate the angular velocity in rad s⁻¹ of the grinding wheel.

261.8 rad s⁻¹ Signup and view all the answers

A rotating wheel required 3.00 s to rotate through 37.0 revolutions. Its angular speed at the end of the 3.00 s interval is 98.0 rad s⁻¹. Calculate the constant angular acceleration of the wheel.

3.27 rad s⁻² Signup and view all the answers

A wheel rotates with a constant angular acceleration of 3.50 rad s⁻². If the angular speed of the wheel is 2.00 rad s⁻¹ at t = 0, through what angular displacement does the wheel rotate in 2.00 s? How many revolutions has the wheel turned during this time interval? What is the angular speed of the wheel at t = 2.00 s?

14.0 rad, 2.23 revolutions, 9.00 rad s⁻¹ Signup and view all the answers

A bicycle wheel is being tested at a repair shop. The angular velocity of the wheel is 4.00 rad s⁻¹ at time t = 0, and its angular acceleration is constant and equal -1.20 rad s⁻². A spoke OP on the wheel coincides with the +x-axis at time t = 0. What is the wheel's angular velocity at t = 3.00 s? What angle in degrees does the spoke OP make with the positive x-axis at this time?

0.40 rad s⁻¹, 25.2° Signup and view all the answers

The bobsled track at the 1994 Olympics in Norway, contained turns with radii of 33 m and 24 m. Find the centripetal acceleration at each turn for a speed of 34 m s⁻¹.

35.1 m s⁻², 48.1 m s⁻² Signup and view all the answers

Imagine that you are a passenger in a car, not wearing a seat belt. The car makes a sharp right turn. What will happen to you?

You will continue to move in a straight line (in the direction you were travelling before the turn), and you will be thrown to the side of the car. Signup and view all the answers

Find the centripetal acceleration of a sample which is at a distance of 5.0 cm from the axis of rotation of a centrifuge rotating at a constant speed of 2000 revolutions per minute.

21991 m s⁻² Signup and view all the answers

A ball of mass 0.35 kg is attached to the end of a horizontal cord and is rotated in a circle of radius 1.0 m on a frictionless horizontal surface. If the cord breaks when the tension in it exceeds 80 N, determine the maximum speed of the ball and the minimum period of the ball.

15.1 ms⁻¹, 0.417 s Signup and view all the answers

A 0.075 kg toy airplane is tied to the ceiling with a string. When the airplane's motor is started it moves with a constant speed of 1.21 m s⁻¹ in a horizontal circle of radius 0.44 m. Find the angle the string makes with the vertical and the tension in the string.

18.7° , 0.826 N Signup and view all the answers

A woman of mass 60 kg stands at the rim of a horizontal turntable having a moment of inertia of 500 kg m² and a radius of 2.00 m. The turntable is initially at rest and is free to rotate about the frictionless vertical axle through its centre. The woman then starts walking around the rim clockwise (as viewed from above the system) at a constant speed of 1.50 m s⁻¹ relative to the Earth. In what direction and with what value of angular speed does the turntable rotate? How much work does the woman do to set herself and the turntable into motion?

The turntable rotates in the opposite direction to the woman, with an angular speed of 0.45 rad s⁻¹. The work done by the woman is 135 J Signup and view all the answers

Determine the angular momentum of the Earth about its rotation axis (assume the Earth is a uniform solid sphere), and about its orbit around the Sun (treat the Earth as a particle orbiting the Sun).

7.07 x 10³³ kg m² s⁻¹, 2.66 x 10⁴⁰ kg m² s⁻¹ Signup and view all the answers

Calculate the magnitude of the angular momentum of the second hand on a clock about an axis through the centre of the clock face. The clock hand has a length of 15.0 cm and a mass of 6.00 kg. Take the second hand to be a thin rod rotating with angular velocity about one end. (Given the moment of inertia of thin rod about the axis through the CM is 1/12 ML²)

1.69 x 10⁻² kg m² s⁻¹ Signup and view all the answers

Study Notes

Exercise 1: Circular Motion

Particle in circular path: A particle moves in a circular path of radius 0.5 m with constant speed of 10 m/s. Calculate the time taken to complete 20 revolutions.
Clock hands' angular velocity: Determine the angular velocities of the hour and minute hands of a clock.
Angular velocity calculation: Calculate the angular velocity of an object in uniform circular motion given its speed and the diameter of the circle.
Revolutions per minute (rpm): A particle completes one revolution in 0.25 seconds. Calculate the number of revolutions per minute (rpm).
Uniform circular motion calculation: A particle moves from one end of a diameter to the other in 3.0 seconds. Find the angular velocity and speed, given the diameter is 5.0 cm.
Constant angular velocity calculation: An object moves in a circle with a radius of 40 cm and constant angular velocity of 6 rad/s. Calculate the velocity of the object and the time for one complete revolution.
Mass in circular motion: A 200 g mass moves in a circle with a radius of 80 cm on a smooth horizontal surface. If it completes 10 revolutions in one second, determine its angular velocity and linear velocity.
Disc rolling calculation: Calculate the number of revolutions and angular displacement of a 30 cm diameter disc that rolls 65 m without slipping.
Angular displacement equation: An equation describes the angular displacement of a swinging door in terms of time. Determine the angular displacement, speed and acceleration at time t = 0 s and t = 3.00 s.
Rotating disk calculation: Calculate the angular speed, tangential speed at a distance of 3.00 cm, radial acceleration, and total distance a point on the rim moves in 2.00 seconds. The disk has a radius of 8.00 cm and rotates at a constant rate of 1200 rev/min.
Grinding wheel calculation: Calculate the angular velocity in rad/s of a 0.35 m diameter grinding wheel rotating at 2500 rpm. Calculate the linear speed and radial/centripetal acceleration of a point at the edge of the wheel.

Exercise 1: Continued (Page 2)

Rotating wheel angular acceleration: A rotating wheel takes 3.00 seconds to complete 37 revolutions, with an angular speed at the end of the interval of 98.0 rad/s. Calculate the constant angular acceleration.
Constant angular acceleration calculation: A wheel rotates with a constant angular acceleration of 3.50 rad/s². Calculate the angular displacement and number of revolutions in 2.00 seconds if the initial angular speed is 2.00 rad/s. Calculate the angular speed at 2.00 seconds.
Bicycle wheel angular velocity: Determine the angular velocity of a bicycle wheel at a specific time (t = 3.00 s) given its angular acceleration and initial velocity. Determine the angle the spoke makes with the positive x-axis.
Centripetal acceleration calculation: Determine the centripetal acceleration of objects moving at a specific speed in turns of a bobsled track with different radii (r = 33 and r = 24 m), given the speed of 34 m/s.

Exercise 1: Continued (Page 3)

Centrifuge calculation: Calculate the centripetal acceleration of a sample in a centrifuge given its distance from the rotation axis and speed.
Rotating ball calculation: Calculate the maximum speed of a ball attached to a string rotated on a horizontal frictionless surface given that the cord breaks when the tension reaches 80 N.
Airplane string angle calculation (inclined plane): An airplane's motor is started, making the airplane move at a constant speed in a horizontal circle. Calculate the angle the string makes with the vertical and the tension in the string.
Turntable calculation: A woman stands on a turntable with a known moment of inertia. Calculate the direction and angular speed of the turntable if the woman walks at a constant speed around the rim of the turntable. Calculate the work done by the woman.
Earth's angular momentum calculation: Calculate the Earth's angular momentum about its rotation axis and its orbit around the Sun.
Clock hand angular momentum calculation: Compute the angular momentum of the second hand of a clock.

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Description

Test your understanding of circular motion with this quiz. You'll calculate time for revolutions, angular velocities, and speeds in various scenarios. Perfect for students studying physics concepts related to circular motion.