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12. Rotational Kinematics

Rotational Velocity & Acceleration

12. Rotational Kinematics

Rotational Velocity & Acceleration

Guided videos.

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Rotational Velocity & Acceleration

Rotational Velocity & Acceleration

Rotational velocity of Earth

Rotational velocity of Earth

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Anderson Video - Non-Uniform Circular Motion

Anderson Video - Non-Uniform Circular Motion

Rotational Motion: Kinematic Equations, Example Problems

Rotational Motion: Kinematic Equations, Example Problems

Step by Step Science

Rotational Motion: An Explanation, Angular Displacement, Velocity and Acceleration

Rotational Motion: An Explanation, Angular Displacement, Velocity and Acceleration

Step by Step Science

Rotational Motion

Rotational Motion

Bozeman Science

Angular Motion and Torque

Angular Motion and Torque

Professor Dave Explains

Angular Velocity and Acceleration

Angular Velocity and Acceleration

Showing 6 of 6 videos

Practice this topic

Multiple Choice

Calculate the rotational velocity (in rad/s) of a clock's minute hand.

EXTRA:Calculate the rotational velocity (in rad/s) of a clock's hour hand.

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Multiple Choice

A wheel of radius 5 m accelerates from 60 RPM to 180 RPM in 2 s. Calculate its angular acceleration.

Has a video solution.

Multiple Choice

A car drives at a constant

15 m / s

along a curve on city street with a radius of

70 m

. What is the acceleration of the car?

Multiple Choice

The dwarf planet Ceres has a radius of

476 km

9.5 \times 10^{20} kg

, and a free fall acceleration due to gravity of

0.28 m / s^{2}

. What speed will a rock have if it is orbiting Ceres, right on the surface? Ceres has no atmosphere – so there are no issues with air resistance – but assume that there are no mountains or large boulders to impede the orbit.

Multiple Choice

A person runs ¼ of the way around a circular lake in 5.6 minutes. What is the person's angular speed?

Textbook Question

FIGURE EX4.24 shows the angular-position-versus-time graph for a particle moving in a circle. What is the particle's angular velocity at (b) t = 4s

Has a video solution.

Textbook Question

Flywheels—rapidly rotating disks—are widely used in industry for storing energy. They are spun up slowly when extra energy is available, then decelerate quickly when needed to supply a boost of energy. A 20-cm-diameter rotor made of advanced materials can spin at 100,000 rpm. b. Suppose the rotor's angular velocity decreases by 40% over 30 s as it supplies energy. What is the magnitude of the rotor's angular acceleration? Assume that the angular acceleration is constant.

Has a video solution.

Textbook Question

The angular velocity of a process control motor is ω = ( 20 ─ ½ t² ) rad/s, where t is in seconds. a. At what time does the motor reverse direction?

Has a video solution.

Textbook Question

A 25 g steel ball is attached to the top of a 24-cm-diameter vertical wheel. Starting from rest, the wheel accelerates at 470 rad/s². The ball is released after ¾ of a revolution. How high does it go above the center of the wheel?

Has a video solution.

Textbook Question

The angular velocity of a spinning gyroscope is measured every 0.5 s. The results and the best-fit line from a spreadsheet are shown in FIGURE P4.63.

a. What is the gyroscope's initial angular velocity, at t = 0 s?

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Textbook Question

FIGURE EX4.36 shows the angular velocity graph of the crankshaft in a car. What is the crankshaft's angular acceleration at (b) t = 3s

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Textbook Question

A computer hard disk 8.0 cm in diameter is initially at rest. A small dot is painted on the edge of the disk. The disk accelerates at 600 rad/s² for ½s, then coasts at a steady angular velocity for another ½s. b. Through how many revolutions has the disk turned?

Has a video solution.

Textbook Question

Your roommate is working on his bicycle and has the bike upside down. He spins the 60-cm-diameter wheel, and you notice that a pebble stuck in the tread goes by three times every second. What are the pebble's speed and acceleration?

Has a video solution.

Textbook Question

A 5.0-m-diameter merry-go-round is initially turning with a 4.0 s period. It slows down and stops in 20 s. (b) How many revolutions does the merry-go-round make as it stops?

Has a video solution.

Textbook Question

Starting from rest, a DVD steadily accelerates to 500 rpm in 1.0 s, rotates at this angular speed for 3.0 s, then steadily decelerates to a halt in 2.0 s. How many revolutions does it make?

Has a video solution.

Textbook Question

The angular velocity of a process control motor is ω = ( 20 ─ ½ t² ) rad/s, where t is in seconds. b. Through what angle does the motor turn between t = 0 s and the instant at which it reverses direction?

Has a video solution.

Textbook Question

A painted tooth on a spinning gear has angular position θ = (6.0 rad/s⁴)t⁴. What is the tooth's angular acceleration at the end of 10 revolutions?

Has a video solution.

Textbook Question

A 6.0-cm-diameter gear rotates with angular velocity ω = ( 20 ─ ½ t² ) rad/s where t is in seconds. At t = 4.0 s, what are: b. The tangential acceleration of a tooth on the gear?

Has a video solution.

Textbook Question

A 6.0-cm-diameter gear rotates with angular velocity ω = ( 20 ─ ½ t² ) rad/s where t is in seconds. At t = 4.0 s, what are: a. The gear's angular acceleration?

Has a video solution.

Textbook Question

CALC A fan blade rotates with angular velocity given by ω_z(t) = g - bt^2, where g = 5.00 rad/s and b = 0.800 rad/s^3. (b) Calculate the instantaneous angular acceleration α_z at t = 3.00 s and the average angular acceleration α_av-z for the time interval t = 0 to t = 3.00 s. How do these two quantities compare? If they are different, why?

Has a video solution.

Textbook Question

CALC A fan blade rotates with angular velocity given by ω_z(t) = g - bt^2, where g = 5.00 rad/s and b = 0.800 rad/s^3. (a) Calculate the angular acceleration as a function of time.

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Textbook Question

CP CALC The angular velocity of a flywheel obeys the equation ω_z(t) = A + Bt2, where t is in seconds and A and B are constants having numerical values 2.75 (for A) and 1.50 (for B). (b) What is the angular acceleration of the wheel at (i) t = 0 and (ii) t = 5.00 s?

Has a video solution.

Textbook Question

CALC The angle θ through which a disk drive turns is given by θ(t) = a + bt - ct^3, where a, b, and c are constants, t is in seconds, and θ is in radians. When t = 0, θ = p/4 rad and the angular velocity is 2.00 rad/s. When t = 1.50 s, the angular acceleration is 1.25 rad/s^2. (c) What are θ and the angular velocity when the angular acceleration is 3.50 rad/s^2?

Has a video solution.

Textbook Question

CALC The angle θ through which a disk drive turns is given by θ(t) = a + bt - ct^3, where a, b, and c are constants, t is in seconds, and θ is in radians. When t = 0, θ = p/4 rad and the angular velocity is 2.00 rad/s. When t = 1.50 s, the angular acceleration is 1.25 rad/s^2. (b) What is the angular acceleration when θ = p/4 rad?

Has a video solution.

Textbook Question

CALC The angle θ through which a disk drive turns is given by θ(t) = a + bt - ct^3, where a, b, and c are constants, t is in seconds, and θ is in radians. When t = 0, θ = p/4 rad and the angular velocity is 2.00 rad/s. When t = 1.50 s, the angular acceleration is 1.25 rad/s^2. (a) Find a, b, and c, including their units.

Has a video solution.

Textbook Question

A car tire is 60 cm in diameter. The car is traveling at a speed of 20 m/s. (c) What is the speed of a point at the bottom edge of the tire?

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Textbook Question

A car tire is 60 cm in diameter. The car is traveling at a speed of 20 m/s. (b) What is the speed of a point at the top edge of the tire?

Has a video solution.

Textbook Question

(II) The angular acceleration of a wheel, as a function of time, is α = 4.2 t² ― 9.0 t , where α is in rad/s² and t in seconds. If the wheel starts from rest (θ = 0 , ω = 0, at t = 0), determine a formula for

(b) the angular position θ, both as a function of time.

Has a video solution.

Textbook Question

(II) Suppose the force Fₜ in the cord hanging from the pulley of Example 10–10, Fig. 10–22, is given by the relation Fₜ = 3.00 t ― 0.20 t² (newtons) where t is in seconds. If the pulley starts from rest, what is the linear speed of a point on its rim 9.0 s later? Ignore friction and use the moment of inertia, calculated in Example 10–10.

Has a video solution.

Showing 29 of 29 practice