Tutorial Rotational Motion

EXERCISE/ROTATIONAL MOTION

ROTATIONAL & CIRCULAR MOTION

1. A computer hard disk normally spins at 7000 rpm. If the hard disk takes 5.0 s to reach this angular velocity staring from rest, calculate:a) The hard disk’s angular acceleration in rad/s2. ( 146.61 rad/s2 )b) The angular displacement of the disk. ( 1832.58 rad )

2. A wheel of radius 50 cm is speeded up uniformly from rest to a speed of 1200 rpm in 30 s. Calculate:a) The angular acceleration of the wheel ( 4.19 rad/s2 )b) The tangential acceleration of a point on its rim. ( 2.10 m/s2 )

3. A wheel 25.0 cm in radius turning at 120 rpm increases its frequency to 600 rpm in 9 s. Find the constant angular acceleration in rads-2. ( 5.58 rad/s2 )

4. A wheel rotates at a constant angular velocity of 1.5 rad/s. What is the angular displacement of a point on rim of the wheel after 2.0 minutes? ( 180 rad )

5. The tires of a Myvi’s car makes 65 revolutions as the car reduces its speed uniformly from 80 km/h to 30 km/h. The tires have a diameter of 0.8 m. What was the angular acceleration of the tires? ( -3.25 rad/s2 )

6. A fan was rotating at 2.0 revolutions per second slows down uniformly and it stops after 5.0 s. Calculate its angular acceleration. ( -2.51 rad/s2 )

7. A wheel of radius 0.40 m starts rotating from rest and after 6.0 s its angular velocity is 3.6 rad/s. What is:

a) The angular acceleration of the wheel? ( 0.6 rad/s2 )b) The angular velocity after 3.0 s? ( 1.8 rad/s )c) The tangential acceleration? ( 0.24 m/s2 )

8. A wheel starts rotating initially from rest with a uniform angular acceleration and complete 1 revolution after t = 6.0 s. Determine:

a) The angular velocity after 6.0 s.b) The angular acceleration.c) The angular velocity after 2 revolutions.d) The time taken for the second revolution.

( 2.09 rad/s , 0.35 rad/s2 , 2.97 rad/s , 8.47 s )

9. The earth takes slightly less than one day to complete one rotation about the axis passing through its poles. The actual time is 8.616 × 104 s. Given this information, what is the angular speed of the Earth about its axis? ( 7.292 × 10-5 rad/s )

ENGINEERING SCIENCE/LGB10203


10. Marilyn is riding in a merry-go-round which is initially at rest. The distance between Marilyn to the center of the merry-go-round is 3.0 m. At t = 0 s is given a constant angular acceleration a = 0.08 rad/s2 for 10.0 s. At t = 10.0 s, find

a) The angular velocity of the merry-go-roundb) The linear velocity that Marilyn feltc) The tangential acceleration of Marilynd) The centripetal acceleration of Marilyne) The total linear acceleration of Marilyn

11. A disk has a moment of inertia of 3.0 × 10-4 kg m2 and is rotating with an angular speed of 3.5 rad/s. What net torque must be applied to bring it to rest within 3 s?

( 3.5 × 10-4 Nm )

12. A wheel is rotating at 2 rad/s when it starts to experience a constant angular acceleration of 3.5 rad/s2. Calculate the number of revolutions it makes in 2 s.

( 1.75 rev )

13. An airplane propeller has a mass of 70 kg and a radius of 75 cm. Find its moment of inertia. How large a torque is needed to give it an angular acceleration of 4.0 rev/s2 ?

(0.99 kNm)

14. As shown in figure below, a constant force of 40 N is applied tangentially to the rim of a wheel with radius 20 cm. The wheel has a moment of inertia of 30 kgm2. Find :

a) The angular acceleration b) The angular speed after 4.0 s from rest c) The number of revolutions made in that 4.0 s

(0.267 rad/s2, 1.1 rad/s, 0.34 rev)

15. The wheel on a grinder is a uniform 0.90 kg disc of 8.0 cm radius. It coasts uniformly to rest from 1400 rpm in a time of 35 s. How large a friction torque slows its motion?

(-1.2 x 10-2 Nm)

16. A shown in figure 1, a mass m = 400 g hangs from the rim of a wheel of radius r = 15 cm. When released from rest, the mass falls 2.0 m in 6.5 s. Find the moment of inertia of the wheel.

(0.92 kg m2)



17. As shown in figure below, a uniform solid sphere rolls on a horizontal surface at 20 m/s and the rolls up the incline. If the friction losses are negligible, what will be the value of h where the ball stops?

(h = 29 m)

( 0.8 rad/s, 2.4 m/s, 0.24 m/s2, 1.92 m/s2, 1.92 m/s2, 1.93 m/s2 )

18. An object with a weight of 50.0 N is attached to the free end of a light string wrapped around a pulley of radius 0.250 m and mass 3.00 kg. The reel is a solid disk, free to rotate in a vertical plane about the horizontal axis passing through its center. The suspended object is released 6.00 m above the floor as shown in figure below.a) Determine the tensional string and acceleration of the system?b) Determine the speed of the object when hits the floor.c) Compare your answer (b) by using the principle of conservation of energy to find

the speed with which the object hits the floor. ( 11.4 N. 9.53 m/s, 9.53 m/s )



19. A cylinder of radius 100 mm and mass 20 kg rolls from rest a distance of 10 m down an inclined plane and in doing so its vertical height decreases by 5 m. What will be the linear velocity of the cylinder after this ?

( 8.1 m/s)

20. A hollow sphere of mass M = 6.0 kg and radius, R = 0.15m rolls without slipping up a ramp at angle θ=30° .The sphere has moved 2.0 m up along the incline before it stop. Find the initial speed of the sphere ?

(3.43 m/s)

21. Calculate the force of the Earth’s gravity on a spacecraft 12800 km ( 2 Earth radii ) above the Earth’ surface if its mass is 1350 kg.

( 1.47 x 103 N )

22. At the surface of a certain planet, the gravitational acceleration g has a magnitude of 12 m/s2. A 21 kg brass ball is transported to this planet. Determine :

a) The mass of the brass ball on the Earth and on the planetb) The weight of the brass ball on the earth and on the planet.

( 21 kg, 21 kg, 206 N, 252 N )

23. Calculate the acceleration due to gravity on the Moon. The Moon’s radius is 1.74 x 106 m and its mass is 7.35 x 1022 kg.

( 1.62 m/s2 )



24. A satellite is placed in a circular orbit to observe the surface of Mars from an altitude of 144 km. The equatorial radius of Mars is 3397 km. If the speed of the satellite is 3480 m/s, what is the magnitude of the centripetal acceleration of the satellite?

( 3.42 m/s2)

25. Callisto and Io are two of Jupiter's satellites. The distance from Callisto to the center of Jupiter is approximately 4.5 times farther than the distance from Io to the center of Jupiter. How does Callisto's orbital period, TC, compare to that of Io, TI?

(TC = 9.5 TI)


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Tutorial Rotational Motion