Physics Chapter 8 concepts
What is the angular speed in rad/s of the second hand of a watch? 1.7 × 10-3 rad/s 6.28 rad/s 0.02 rad/s 60 rad/s 0.10 rad/s
0.10 rad/s
Between t= 0 s and t= 10 s, about how many revolutions does the merry-go-round complete? 1 2 3 4
2
Two points are located on a rigid wheel that is rotating with decreasing angular velocity about a fixed axis. Point A is located on the rim of the wheel and point B is halfway between the rim and the axis. Which one of the following statements concerning this situation is true? The angular velocity at point A is greater than that of point B. Each second, point A turns through a greater angle than point B. Both points have the same centripetal acceleration. Both points have the same instantaneous angular velocity. Both points have the same tangential acceleration.
Both points have the same instantaneous angular velocity.
A bicycle is turned upside down, the front wheel is spinning (see the drawing), and there is an angular acceleration. At the instant shown, there are six points on the wheel that have arrows associated with them. Which one of the following quantities could the arrows not represent? Tangential velocity Centripetal acceleration Tangential acceleration
Centripetal acceleration
As an object rotates, its angular speed increases with time. Complete the following statement: The total acceleration of the object is given by the angular acceleration. the vector sum of the angular velocity and the tangential acceleration divided by the elapsed time. the vector sum of the centripetal acceleration and the tangential acceleration. the tangential acceleration. the centripetal acceleration.
the vector sum of the centripetal acceleration and the tangential acceleration.
Let v1 and v2 denote the linear speed of child 1 and child 2, respectively. Which of the following is true? v1>v2 v1=v2 v1<v2
v1>v2
Which equation is valid only when the angular measure is expressed in radians? ω2=ω20+2αθ ω=Δθ/Δt θ=1/2αt2+ω0t ω=vT/r α=Δω/Δt
ω=vT/r
A long thin rod of length 2L rotates with a constant angular acceleration of 8.0 rad/s2 about an axis that is perpendicular to the rod and passes through its center. What is the ratio of the angular speed (at any instant) of a point on the end of the rod to that of a point a distance L/2 from the end of the rod? 1:2 1:1 1:4 4:1 2:1
1:1
A wheel of radius 0.5 m rotates with a constant angular speed about an axis perpendicular to its center. A point on the wheel that is 0.2 m from the center has a tangential speed of 2 m/s. Determine the angular speed of the wheel. 10 rad/s 4.0 rad/s 20 rad/s 0.4 rad/s 2.0 rad/s
10 rad/s
A drill bit in a hand drill is turning at 1200 revolutions per minute (1200 rpm). Express this angular speed in radians per second (rad/s). 126 rad/s 2.1 rad/s 0.67 rad/s 39 rad/s 19 rad/s
126 rad/s
A bicycle with wheels of radius 0.4 m travels on a level road at a speed of 8 m/s. What is the angular speed of the wheels? 10 rad/s (10 π) rad/s 20 rad/s ( π/10) rad/s (20/ π) rad/s
20 rad/s
A long thin rod of length 2L rotates with a constant angular acceleration of 8.0 rad/s2 about an axis that is perpendicular to the rod and passes through its center. What is the ratio of the centripetal acceleration of a point on the end of the rod to that of a point a distance L/2 from the end of the rod? 4:1 1:4 1:2 2:1 1:1
2:1
A long thin rod of length 2L rotates with a constant angular acceleration of 8.0 rad/s2 about an axis that is perpendicular to the rod and passes through its center. What is the ratio of the tangential acceleration of a point on the end of the rod to that of a point a distance L/2 from the end of the rod? 1:2 1:1 1:4 2:1 4:1
2:1
Correct answer iconCorrect. A long thin rod of length 2L rotates with a constant angular acceleration of 8.0 rad/s2 about an axis that is perpendicular to the rod and passes through its center. What is the ratio of the tangential speed (at any instant) of a point on the end of the rod to that of a point a distance L/2 from the end of the rod? 2:1 1:2 1:1 1:4 4:1
2:1
Complete the following statement: The angular measure 1.0 radian is equal to 57.3°. 0.0175°. 1.57°. 6.28°. 3.14°.
57.3
A rotating object has an angular acceleration α that is not zero. Which one or more of the following three statements is consistent with a non-zero angular acceleration? A. The angular velocity ω increases as time passes.B. The angular velocity ω has the same value at all times.C. The angular velocity ω decreases as time passes. A and B, but not C A, B, and C A and C, but not B A only B and C, but not A
A and C, but not B
A car is up on a hydraulic lift at a garage. The wheels are free to rotate, and the drive wheels are rotating with a constant angular velocity. Which one of the following statements is true? A point on the rim has no tangential and no centripetal acceleration. A point on the rim has both a nonzero tangential acceleration and a nonzero centripetal acceleration. A point on the rim has a nonzero tangential acceleration but no centripetal acceleration. A point on the rim has no tangential acceleration but does have a nonzero centripetal acceleration.
A point on the rim has no tangential acceleration but does have a nonzero centripetal acceleration.
A rotating object has an angular acceleration of α = 0 rad/s2. Which one or more of the following three statements is consistent with a zero angular acceleration? A. The angular velocity is ω = 0 rad/s at all times.B. The angular velocity is ω = 10 rad/s at all times.C. The angular displacement θ has the same value at all times. B only A, B, and C A and B, but not C C only A only
B only
Three objects are visible in the night sky. They have the following diameters (in multiples of d) and subtend the following angles (in the multiples of θ0) at the eye of the observer. Object A has a diameter of 4d and subtends an angle of 2θ0. Object B has a diameter of 3d and subtends an angle of θ0/2. Object C has a diameter of d/2 and subtends an angle of θ0/8. Rank them in descending order (greatest first) according to their distance from the observer. B, C, A A, B, C C, A, B B, A, C
B,C,A
A circular hula hoop rolls upright without slipping on a flat horizontal surface. Which one of the following statements is necessarily true? Every point on the rim of the wheel has a different velocity. All points on the rim of the hoop have acceleration vectors that are tangent to the hoop. All points on the rim of the hoop have acceleration vectors that point toward the center of the hoop. All points on the rim of the hoop have the same speed. All points on the rim of the hoop have the same velocity.
Every point on the rim of the wheel has a different velocity.
The jet engine has angular acceleration of -2.5 rad/s2. Which one of the following statements is correct concerning this situation (Assume counterclockwise is positive.) If the angular velocity is clockwise, then its magnitude must increase as time passes. The direction of the angular velocity must be clockwise. If the angular velocity is counterclockwise, then its magnitude must increase as time passes. The direction of the angular acceleration is counterclockwise. The angular velocity must be decreasing as time passes.
If the angular velocity is clockwise, then its magnitude must increase as time passes.
This can be done by adjusting the angular speed of the space station, so the centripetal acceleration at an astronaut's feet equals g, the magnitude of the acceleration due to the earth's gravity. If such an adjustment is made, what will be true about the acceleration at the astronaut's head due to the artificial gravity? It will be greater than g. It will be equal to g. It will be less than g.
It will be less than g.
The SI unit for angular displacement is the radian. In calculations, what is the effect of using the radian? The result of the calculation will always have the radian among the units. Any angular quantities involving the radian must first be converted to degrees. Since the radian is a unitless quantity, there is no effect on other units when multiplying or dividing by the radian. Since the radian is a unitless quantity, the number of radians of angular displacement plays no role in the calculation. Since the radian is a unitless quantity, any units multiplied or divided by the radian will be equal to one.
Since the radian is a unitless quantity, there is no effect on other units when multiplying or dividing by the radian.
Which one of the following statements correctly relates the centripetal acceleration and the angular velocity? The centripetal acceleration is the product of the radius and the square of the angular velocity. The centripetal acceleration is the product of the radius and the angular velocity. The centripetal acceleration is the angular velocity divided by the radius. The centripetal acceleration is independent of the angular velocity. The centripetal acceleration is the square of the angular velocity divided by the radius.
The centripetal acceleration is the product of the radius and the square of the angular velocity.
It is possible to build a clock in which the tips of the hour hand and the second hand move with the same tangential speed. This is normally never done, however. Why? The length of the hour hand would be 720 times smaller than the length of the second hand. The hour hand and the second hand would have the same length. The length of the hour hand would be 720 times greater than the length of the second hand.
The length of the hour hand would be 720 times greater than the length of the second hand.
A rigid body rotates about a fixed axis with a constant angular acceleration. Which one of the following statements is true concerning the tangential acceleration of any point on the body? The tangential acceleration is constant in both magnitude and direction. The tangential acceleration depends on the angular velocity. The tangential acceleration is equal to the centripetal acceleration. The tangential acceleration depends on the change in the angular velocity. The tangential acceleration is zero m/s2.
The tangential acceleration depends on the change in the angular velocity.
Which one of the following statements concerning a wheel undergoing rolling motion is true? The tangential velocity is the same for all points on the rim of the wheel. The angular acceleration of the wheel must be zero m/s2. There is no slipping at the point where the wheel touches the surface on which it is rolling. The tangential velocity is the same for all points on the wheel. The linear velocity for all points on the rim of the wheel is non-zero.
There is no slipping at the point where the wheel touches the surface on which it is rolling.
A satellite follows a circular path with constant speed around a planet. Which one of the following quantities is constant and non-zero for this satellite? centripetal acceleration angular velocity linear velocity angular acceleration total acceleration
angular velocity
The wheels of a NASCAR racer roll without slipping as the car moves in a circular path at constant speed. Which one of the following quantities has a non-zero value and has a constant value in this situation? centripetal acceleration total acceleration angular velocity angular acceleration
angular velocity
A thin rod rotates at a constant angular speed. In case A the axis of rotation is perpendicular to the rod at its center. In case B the axis is perpendicular to the rod at one end. In which case, if either, are there points on the rod that have the same tangential speeds? case A case B both
case a
The moon is 3.85 × 108 m from the earth and has a diameter of 3.48 × 106 m. You have a pea (diameter = 0.50 cm) and a dime (diameter = 1.8 cm). Close one eye and hold each object at arm's length (71 cm) between your open eye and the moon. Which objects, if any, completely cover your view of the moon? Assume that the moon and both objects are sufficiently far from your eye that the given diameters are equal to arc lengths when calculating angles. Pea Neither Both Dime
dime
The scalar angular acceleration is the rate of change of the angular speed with time. Which graph best represents the merry-go-round's scalar angular acceleration between t = 0 s and t = 20 s?
graph c (z shape)
You are in a tall building located near the equator. As you ride an elevator from the ground floor to the top floor, your tangential speed due to the earth's rotation ____________. increases when the speed of the elevator increases and decreases when the speed of the elevator decreases increases does not change decreases
increases
The speedometer of a truck is set to read the linear speed of the truck, but uses a device that actually measures the angular speed of the rolling tires that came with the truck. However, the owner replaces the tires with larger-diameter versions. Does the reading on the speedometer after the replacement give a speed that is less than, equal to, or greater than the true linear speed of the truck? less than equal to greater than
less than
Between t = 30 s and t = 40 s, the merry-go-round: rotates clockwise, at a constant rate. rotates clockwise, and slows down. rotates counterclockwise, at a constant rate. rotates counterclockwise, and slows down.
rotates clockwise, and slows down.
Between t = 10 s and t = 20 s, the merry-go-round: rotates clockwise, at a constant rate. rotates clockwise, and slows down. rotates counterclockwise, at a constant rate. rotates counterclockwise, and slows down.
rotates counterclockwise, and slows down.
For a given circle, the radian is defined as which one of the following expressions? the arc length divided by the circumference of the circle two times ninety degrees divided by π (3.141592...) π (3.141592...) times twice the radius of the circle the arc length divided by the diameter of the circle the arc length divided by the radius of the circle
the arc length divided by the radius of the circle
Consider the following situation: one of the wheels of a motor cycle is initially rotating at 39 rad/s. The driver then accelerates uniformly at 7.0 rad/s2 until the wheels are rotating at 78 rad/s. Which one of the following expressions can be used to find the angular displacement of a wheel during the time its angular speed is increasing? Consider the following situation: one of the wheels of a motor cycle is initially rotating at 39 rad/s. The driver then accelerates uniformly at 7.0 rad/s2 until the wheels are rotating at 78 rad/s. Which one of the following expressions can be used to find the angular displacement of a wheel during the time its angular speed is increasing?
w2 = W02+2aθ
A wheel of radius 0.5 m rotates with a constant angular speed about an axis perpendicular to its center. A point on the wheel that is 0.2 m from the center has a tangential speed of 2 m/s. Determine the tangential acceleration of the point that is 0.2 m from the center. 0.4 m/s2 10 m/s2 2.0 m/s2 zero m/s2 4.0 m/s2
zero m/s2
A wheel rotates with a constant angular speed ω. Which one of the following is true concerning the angular acceleration α of the wheel, the tangential acceleration aT of a point on the rim of the wheel, and the centripetal acceleration ac of a point on the rim? α = 0 rad/s2, aT = 0 m/s2, and ac = 0 m/s2 α = 0 rad/s2, aT = 0 m/s2, and ac ≠ 0 m/s2 α ≠ 0 rad/s2, aT ≠ 0 m/s2, and ac ≠ 0 m/s2 α = 0 rad/s2, aT ≠ 0 m/s2, and ac = 0 m/s2 α ≠ 0 rad/s2, aT = 0 m/s2, and ac = 0 m/s2
α = 0 rad/s2, aT = 0 m/s2, and ac ≠ 0 m/s2
An electric clock is hanging on a wall. As you are watching the second hand rotate, the clock's battery stops functioning, and the second hand comes to a halt over a brief period of time. Which one of the following statements correctly describes the angular velocity ω and angular acceleration α of the second hand as it slows down? ω and α are both negative. ω is positive and α is negative. ω is negative and α is positive. ω and α are both positive.
ω is negative and α is positive.
Equation 8.7 (θ=ω0t+12αt2θ=ω0t+12αt2) is being used to solve a problem in rotational kinematics. Which one of the following sets of values for the variables ω0, α, and t cannot be substituted directly into this equation to calculate a value for θ? ω0 = 0.16 rev/s, α = 0.29 rev/s2, and t = 3.8 s. ω0 = 1.0 rad/s, α = 1.8 rad/s2, and t = 3.8 s. ω0 = 0.16 rev/s, α = 1.8 rad/s2, and t = 3.8 s.
ω0 = 0.16 rev/s, α = 1.8 rad/s2, and t = 3.8 s.