Q: A rotating amusement ride has a radius of $$r = 31 m $$and angular speed $$\omega = 6.39 \times 10$$^{-2}$$ rad/s. What is the linear speed v$ of a rider at the rim?

$$v = 31 \times 6.39 \times 10$$^{-2}$$

Question 1

A rigid body rotates about a fixed axis. Which statement best describes the motion of every point on the body during pure rotation?

Accepted Answer

Every point moves in a circle whose center lies on the axis of rotation.

Question 2

The angular position $$	heta of a $$reference line on a rotating disk is given by $$	heta = s / r. If $$the arc length $$s is$$ $$6.28 m $$and the radius $$r is$$ $$1 m$$, what is the angular position in radians?

Accepted Answer

$$	heta = 6.28$$ rad

Question 3

A wheel rotates from angular position $$\$$theta_1$$ = 2$$ rad to $$\$$theta_2$$ = 5$$ rad. What is the angular displacement $$\Delta 	heta$$?

Accepted Answer

$$\Delta 	heta = 3$$ rad

Question 4

If a rotating body has an angular velocity $$\omega$$ that is not constant, which of the following is true?

Accepted Answer

The body has a nonzero angular acceleration $$\alpha.$$

Question 5

A child’s top is spun with angular acceleration $$\alpha = 5t^2$ - 4t$$, where $$t is in $$seconds. What is the expression for the angular velocity $$\omega(t)$$, given that $$\omega(0) = 5$$ rad/s?

Accepted Answer

$$\omega(t) = \frac{5}{3}t^3$ - 2t^2$ + 5$$

Question 6

A point on a rotating disk is at a distance $$r$$ from the axis. If the disk rotates through an angle $$	heta$$, what is the arc length $$s$$ traveled by the point?

Accepted Answer

$$s = r 	heta$$

Question 7

A Ferris wheel rotates with a constant angular speed $$\omega. $$What is the period $$T of $$one revolution for a point on the rim?

Accepted Answer

$$T = 2\pi / \omega$$

Question 8

The linear speed $$v of a $$point on a rotating body is related to the angular speed $$\omega$$ and the radius $$r by $$which equation?

Accepted Answer

$$v = \omega r$$

Question 9

A particle moves in a circle of radius $$r$$ with angular acceleration $$\alpha. $$What is the tangential component of its linear acceleration $$a_t$$?

Accepted Answer

$$a_t = r \alpha$$

Question 10

A rider on a rotating ring experiences both tangential and radial acceleration. If the tangential acceleration is $$a_t$$ and the radial acceleration is $$a_r$$, what is the magnitude of the total acceleration $$a$$?

Accepted Answer

$$a = \sqrt{a_t^2$ + a_r^2$}$$

Question 11

A disk rotates such that its angular position is given by $$	heta(t) = -1.00 - 0.500t^2$ + 2.00t. $$What is the angular velocity $$\omega(t)$$?

Accepted Answer

Question 12

A particle moves in a circle of radius $$r$$ with linear speed $$v. $$What is the radial (centripetal) acceleration $$a_r$$?

Accepted Answer

$$a_r = v^2$ / r$$

Question 13

If a rotating object’s angular velocity changes from $$\$$omega_1$$ to $$\$$omega_2$$ over a time interval $$\Delta t$$, what is the average angular acceleration $$\alpha_{avg}$$?

Accepted Answer

$$\alpha_{avg} = (\$$omega_2$$ - \$$omega_1$$) / \Delta t$$

Question 14

A rotating amusement ride has a radius of $$r = 31 m $$and angular speed $$\omega = 6.39 	imes 10$$^{-2}$$ rad/s. What is the linear speed v$ of a rider at the rim?

Accepted Answer

$$v = 31 	imes 6.39 	imes 10$$^{-2}$$

Question 15

A disk rotates such that its angular position is $$	heta(t) = -1.00 - 0.500t^2$ + 2.00t. $$What is the angular acceleration $$\alpha(t)$$?

Accepted Answer

Rotation: Rotational Variables and Their Relationship to Linear Motion

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