Rotational Kinematics Notes + Practice Calculus Based

Multiple Choice

What does the slope of a $$\theta$$  vs t graph represent?

• The angular acceleration ( $$\alpha$$  )

• The angular velocity ( $$\omega$$  )

• The angular displacement ( $$\Delta\theta$$  )

• The torque ( $$\tau$$  )

Multiple Choice

A solid cylinder of mass m and radius R has a string wound around it. A person holding the string pulls it vertically upward, as shown above, such that the cylinder is suspended in midair for a brief time interval Δt and its center of mass does not move. The tension in the string is T, and the rotational inertia of the cylinder about its axis is 1/2 mR². The linear acceleration of the person's hand during the time interval Δt is

• (T - mg)/m

• 2g

• g/2

• T/m

• zero

Multiple Choice

What is the difference between rotational motion and linear motion as described in the text?

• Rotational motion involves pivoting around a point, while linear motion is straight movement.

• Rotational motion is faster than linear motion.

• Linear motion is only applicable to point particles, while rotational motion applies to all objects.

• There is no difference; both are the same.

Multiple Choice

A uniform rod is hinged at the one end (the dark dot on the left). What is the magnitude and direction of the net torque on the rod?

• 75 mN clockwise

• 75 mN counter clockwise

• 325 mN Counterclockwise

• 325 mN clockwise

• 75 N counter clockwise

Multiple Choice

What is the axis of rotation when spinning a donut around its center?

• In the donut hole

• Around the outer edge

• Through the icing

• At the bottom of the donut

Multiple Choice

What are the key differences between linear motion and rotational motion as described in the text?

• Linear motion is described by angular displacement

• Rotational motion is described by displacement

• Linear motion involves velocity and acceleration

• Rotational motion involves angular velocity and angular acceleration

Multiple Choice

What is the significance of the number 360 in relation to circles?

• It is based on the ancient Babylonians' number system.

• It is derived from the Persian calendar.

• It has no relation to the geometry of the circle.

• It is the equivalent of the displacement unit.

Multiple Choice

​ θ indicates the angle through which an object has rotated.  It is measured in radians.

• Angular Displacement
• Average Angular Velocity
• Instantaneous Angular Velocity
• Angular acceleration

Multiple Choice

A radian is all of the following EXCEPT

• A dimensionless quantity
• The ratio of arc length over radius
• The same as degrees
• The unit for rotational position

Multiple Choice

An object rotates through 90 degrees. What is it's angular displacement in radians? ( Hint: 2Pi radians = 360 degrees )

• 90

• Pi

• Pi/2

• 2Pi

Multiple Choice

What is the formula for angular displacement?

• θ = s/r

• θ = r/s

• θ = s*r

• θ = r+s

Multiple Choice

Convert $$90^\circ$$ to radians.

• $$\frac{\pi}{2}$$

• $$\frac{\pi}{3}$$

• $$\frac{\pi}{4}$$

• $$\pi$$

Multiple Choice

What happens to points A and B as the disk rotates?

• They cover the same arc length

• They cover different angles

• They cover the same angle but different arc lengths

• They do not move

Multiple Choice

What is the angular displacement for an arc length (s) that is equal to the radius of the circular rigid body?

• 0.5 rad

• 1.0 rad

• 0.5π rad

• 1.0π rad

• 1.5π rad

Multiple Choice

A record spins 4 times around its center. It makes 4 revolutions. How many radians did it pass?

• π rad

• 2π rad

• 4π rad

• 6π rad

• 8π rad

Multiple Choice

A circular hoop of radius 0.86 m rotates π/3 rad about its center. A small bug is on the hoop - what distance does it travel (arc length) during this rotation?

• 0.30 m

• 0.90 m

• 1.4 m

• 2.7 m

Multiple Choice

What linear displacement is covered by Person A and Person B on the merry-go-round?

• 1.8 m for Person A and 2.7 m for Person B

• 2.3 m for Person A and 3.4 m for Person B

• 1.5 m for Person A and 2.5 m for Person B

• 2.0 m for Person A and 3.0 m for Person B

Multiple Choice

What are the equations that relate angular velocity and angular acceleration to their linear equivalents?

• v = dx/dt, a = dv/dt

• v = dθ/dt, a = dω/dt

• v = dθ/dt, a = dθ/dt

• v = dx/dt, a = dθ/dt

Multiple Choice

The graph shows the angular velocity as a function of time for a point on a rotating disk. The magnitude of theangular acceleration of the disk at is most nearly

• $$1.5\ \frac{rad}{s^2}$$

• $$5\ \frac{rad}{s^2}$$

• $$2\ \frac{rad}{s^2}$$

• $$20\ \frac{rad}{s^2}$$

Multiple Choice

If the translational velocity (v) of an object is 3 m/s, and is located a distance of 2 m from the axis of rotation, what is the object's angular velocity (ω)?

• 0.67 rad/s
• 1.5 rad/s
• 5 rad/s
• 6 rad/s

Multiple Choice

What is the relationship between angular velocity and linear velocity as described in the image?

• Angular velocity is always greater than linear velocity

• Linear velocity is independent of angular velocity

• Linear velocity increases as the radius increases

• Angular velocity and linear velocity are unrelated

Multiple Choice

What is the relationship between angular acceleration (α) and linear acceleration (a) as shown in the equations?

• α = a/r

• a = rα

• α = dω/dt

• a = d(v/r)/dt

Multiple Choice

What is the relationship between angular displacement (θ) and linear displacement (s)?

• s = rθ

• s = θ/r

• s = r/θ

• s = θ^2

Multiple Choice

A sphere rotates about its axis, starting at θ = 0 rad and finishing at θ = 3.2 rad in 4.2 s. What is its average angular velocity?

• 0.38 rad/s

• 0.76 rad/s

• 1.1 rad/s

• 1.3 rad/s

• 2.6 rad/s

Multiple Choice

What is the angular acceleration of a ball that starts at rest and increases its angular velocity uniformly to 5 rad/s in 10 s?

• 0.5 rad/s²

• 1.0 rad/s²

• 1.5 rad/s²

• 2.0 rad/s²

• 2.5 rad/s²

Multiple Choice

A plate revolves about its center on a spindle with an angular velocity ω = 2.0 rad/s. What is the linear velocity of a point that is 0.032 m from the axis of rotation?

• 0.008 m/s

• 0.016 m/s

• 0.032 m/s

• 0.048 m/s

Multiple Choice

A plate increases its angular velocity about its center on a spindle with an angular acceleration α = 1.5 rad/s². What is the linear acceleration of a point that is 2.000 m from the axis of rotation?

• 0.0080 m/s²

• 0.016 m/s²

• 0.032 m/s²

• 0.048 m/s²

• 0.064 m/s²

Multiple Choice

What is the angular displacement of the disc at t = 6 seconds?

• -18 rad

• -9.0 rad

• 0 rad

• 9.0 rad

• 18 rad

Multiple Choice

What is the angular velocity of the disc at 3.0 s?

• -18 rad/s

• -9.0 rad/s

• 0 rad/s

• 9.0 rad/s

• 18 rad/s

Multiple Choice

A turnable begins to rotate from rest with a constant angular acceleration. If a point on the edge of the turntable travels 9 radians during a 3.0 second time period, the angular acceleration of the turntable is

• 2.0 s^-2

• 3.0 s^-2

• 4.0 s^-2

• 6.0 s^-2

• 9.0 s^-2

Multiple Choice

A 0.12-m-radius grinding wheel takes 5.5 s to speed up from 2.0 rad/s to 11.0 rad/s. What is the wheel's average angular acceleration?

• 0.20 rad/s/s

• 4.81 rad/s/s

• 3.12 rad/s/s

• 1.63 rad/s/s

Multiple Choice

What is angular acceleration?

• How far an object rotates at a given speed

• The change in angular velocity divided by time

• Same as linear acceleration

• The change in linear velocity divided by time

Multiple Choice

A dics starts to rotate with an angular velocity of  rad/s² . find its angular speed after 4s?  

• $$2\pi\ \frac{rad}{s}$$

• $$6\pi\ \frac{rad}{s}$$

• $$8\pi\ \frac{rad}{s}$$

• $$4\pi\ \frac{rad}{s}$$