Rotation Kinematics Extra Practice + Notes Algebra Based

Multiple Choice

A grindstone spinning at the rate of 8.3 rev/s has what approximate angular velocity? ( HINT: 1 revolution = 2Pi radians and Pi ~ 3.14 )

• 3.2 rad/s

• 26 rad/s

• 52 rad/s

• 81 rad/s

Multiple Choice

The graph shows the angular velocity $$\omega$$ as a function of time $$t$$ for a point on a rotating disk. The magnitude of the angular acceleration of the disk $$t=2\ s$$ is most nearly

• $$0.7\ \frac{rad}{s^2}$$

• $$1.5\ \frac{rad}{s^2}$$

• $$2\ \frac{rad}{s^2}$$

• $$20\ \frac{rad}{s^2}$$

Multiple Choice

A fan blade, initially at rest, rotates with a constant acceleration of 0.025 rad/s². What is the time interval required for it to reach a 4.2 rad displacement after starting from rest

• 12.96 s

• 168 s

• 336 s

• 18.33 s

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

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

• $$\frac{\pi}{2}$$

• $$\frac{\pi}{3}$$

• $$\frac{\pi}{4}$$

• $$\pi$$

Multiple Choice

What is the relationship between the angle θ, the radius r, and the arc length s in a circle?

• s = rθ

• s = θ/r

• s = θ + r

• s = r - θ

Multiple Choice

What is the relationship between arc length (s), radius (r), and angle (θ) in a circle?

• Arc length is equal to the radius times the angle

• Arc length is equal to the angle divided by the radius

• Arc length is equal to the radius divided by the angle

• Arc length is equal to the angle times the radius

Multiple Choice

Define the angle of rotation, θ, as the ratio of the arc length, s, to the radius r of the circle. What is the formula for θ?

• θ = s/r

• θ = r/s

• θ = s + r

• θ = s - r

Multiple Choice

How many radians make up one revolution of 360 degrees?

• π/2

• π

• 2π

• 3π/2

Multiple Choice

What is the relationship between radians and degrees as shown in the image?

• 1 radian = 180 degrees

• 1 radian = 57.3 degrees

• 1 radian = 360 degrees

• 1 radian = 90 degrees

Multiple Choice

How many radians are subtended by a 0.20 m arc of a circle of radius 0.80 m?

• 0.25 rad

• 0.5 rad

• 1 rad

• 1.5 rad

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

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

• 90

• Pi

• Pi/2

• 2Pi

Open Ended

How many degrees are in π/3 radians?

Multiple Choice

Convert $$\frac{7\pi}{6}$$ radians to degrees.

• $$180^\circ$$

• $$210^\circ$$

• $$240^\circ$$

• $$270^\circ$$

Multiple Choice

What is the angle inside a circle, in radians, that subtends an arc length of 0.25 m? The radius of the circle is 5.0 m.

• 0.01 rad

• 0.03 rad

• 0.05 rad

• 0.08 rad

Multiple Choice

What is the value of π/2 radians in degrees?

• 0°

• 45°

• 90°

• 180°

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

• 0.5 π rad

• 1.0 π rad

Multiple Choice

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

• π rad

• 2π rad

• 4π 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?

• 0.24 m

• 0.71 m

• 0.90 m

• 1.18 m

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

• $$1.5\ \frac{rad}{s^2}$$

• $$5\ \frac{rad}{s^2}$$

• $$2\ \frac{rad}{s^2}$$

• $$20\ \frac{rad}{s^2}$$