A Ferris wheel in Japan has a radius of 50m and a mass of 1.2 x 10 6 kg. If a torque of 1 x 10 9 Nm is needed to turn the wheel when it starts at

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Anastasia Price
5 years ago
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1 Option B Quiz

2 1. A Ferris wheel in Japan has a radius of 50m and a mass of 1. x 10 6 kg. If a torque of 1 x 10 9 Nm is needed to turn the wheel when it starts at rest, what is the wheel s angular acceleration? I mr rad / s

3 . A 08 N force is applied tangentially to the surface of a ball of string that has a radius of m in order to give it an angular acceleration of 0.03 rad/s. What is the ball s moment of inertia? FR I I I FR (08N)(m) 13000kgm 0.03rad / s

4 3. When she is launched from a springboard, a diver's angular speed about her center of mass changes from zero to 6.0 rad/s in 0 ms. Her rotational inertia about her center of mass is constant at 1.0 kg m. During the launch, what are the magnitudes of (a) her average angular acceleration the average external torque on her from the board? f t f i t 6.rad / s 0.s i 8.rad / s I (1kgm )(8.rad / s ) 338Nm

5 4. A force is applied in the direction perpendicular to the handle of the wrench and at the end of the handle. Find the force given the torque is 15 Nm and the length of the wrench is 0.5 m. FR F R N

6 5. A wheel rotating at 15.0 rad/s undergoes an angular acceleration of 10.0 rad/s. Through what angle has the wheel turned when t = 5.00 s? it 1 t (15rad / s)(5s) 00rads 1 (10rad / s )(5s)

7 6. A wheel, initially rotating at 10.0 rad/s, undergoes an angular acceleration of 5.00 rad/s. What is the angular velocity when the wheel has turned through an angle of 50.0 rad? f i f f 10 (5)(50) 4.5rad / s

8 7. The horizontal uniform rod shown above has length 0.60 m and mass.0 kg. The left end of the rod is attached to a vertical support by a frictionless hinge that allows the rod to swing up or down. The right end of the rod is supported by a cord that makes an angle of 30 with the rod. A spring scale of negligible mass measures the tension in the cord. A 0.50 kg block is also attached to the right end of the rod. On the diagram below, draw and label vectors to represent all the forces acting on the rod. Show each force vector originating at its point of application. T F H 30 o F V W rod W block

9 Calculate the reading on the spring scale. Rotational equilibrium: S FRsin = 0 T T T d T sin W (kg)(9.8m / s 9.4N rod d r W block d )(.3m) (0.5kg)(9.8m / o (0.6)sin 30 b s )(.6m) 0.6 m T sin 30 o F H 0.3 m 0.3 m F V W rod W block

10 C. Calculate the magnitude of the force exerted by the hinge on the rod. Translational Equilibrium F F F F F F F V V V V H H H T sin 30 Wrod Wblock 0 T sin 30 Wrod Wblock 9.4(sin 30) ()(9.8) (0.5)(9.8) 9.8N T cos 9.4 cos30 5.5N F H F V T 30 o T cos 30 o W rod W block T sin 30 o 9.4 N sin 30 o W rod = kg * 9.8 ms - W block =.5kg * 9.8 ms - F V

11 8. A kg record with a radius of 15 cm rotates with an angular speed of 33 1 / 3 rpm. Find the angular momentum of the record. linear momentum: p mv roational momentum: L I I I 33.3rev 1min rad min 60s rev L I L 1 mr kgm 3.49rad / s L ( disk) 1 (0.015kg)(0.15m) kgm Ns I 3.49rad / s

12 9. Consider a motor that exerts a constant torque of 5.0 N m to a horizontal platform whose moment of inertia is 50.0 kg m. Assume that the platform is initially at rest and the torque is applied for 1.0 rotations. a. How much work does the motor do on the platform during this process? linear: W = Fd rotational: W = 1 rotations = 4 rad W = (5.0 N m)(4 rad) = 1885 J

13 9. Consider a motor that exerts a constant torque of 5.0 N m to a horizontal platform whose moment of inertia is 50.0 kg m. Assume that the platform is initially at rest and the torque is applied for 1.0 rotations. b. What is the angular velocity ω f of the platform at the end of this process? = I = / I = (5 N m)/(50 kg m ) = 0.5 rad/s f = i + i = 0 rad/s ω = αθ = (0.5)(4π) = 8.68 rad/s

14 9. Consider a motor that exerts a constant torque of 5.0 N m to a horizontal platform whose moment of inertia is 50.0 kg m. Assume that the platform is initially at rest and the torque is applied for 1.0 rotations. c. What is the rotational kinetic energy, E k,rot of the platform at the end of the process described above? E K = ½ mv E k,rot = 1 Iω (linear) (rotational) E k,rot = 1 (50kg m )(8.68 rad/s) E k,rot = 1885 J

15 9. Consider a motor that exerts a constant torque of 5.0 N m to a horizontal platform whose moment of inertia is 50.0 kg m. Assume that the platform is initially at rest and the torque is applied for 1.0 rotations. d. How long does it take for the motor to do the work done on the platform calculated in Part A? ω f = ω i + αt 8.68 rad s = rad s t = = 17.36s t

16 9. Consider a motor that exerts a constant torque of 5.0 N m to a horizontal platform whose moment of inertia is 50.0 kg m. Assume that the platform is initially at rest and the torque is applied for 1.0 rotations. e. What is the average power delivered by the motor in the situation above? power = W/t linear power = W/t rotational P avg = W 1885 J = = 108.3Watts t 17.4s

17 9. Consider a motor that exerts a constant torque of 5.0 N m to a horizontal platform whose moment of inertia is 50.0 kg m. Assume that the platform is initially at rest and the torque is applied for 1.0 rotations. f. Note that the instantaneous power P delivered by the motor is directly proportional to ω, so P increases as the platform spins faster and faster. How does the instantaneous power P f being delivered by the motor at the time t f compare to the average power P avg calculated in Part e? P f = τω f = 5N m P f P avg = 17 W 108 W = 8.68 rad s = 17 Watts

We define angular displacement, θ, and angular velocity, ω. What's a radian?

We define angular displacement, θ, and angular velocity, ω Units: θ = rad ω = rad/s What's a radian? Radian is the ratio between the length of an arc and its radius note: counterclockwise is + clockwise