## Circular Motion Problems

1. Calculate the angular speed of the second hand, minute hand and hour hand of a clock.
2. What is the angular velocity of the minute hand of a clock? What is the angular displacement of the minute hand in 20 minutes? If the minute hand is 5 cm long, what is the linear velocity of its tip?
3. What is angular displacement of the minute hand of a clock in 25 minutes?
4. What is the angular velocity of a second hand of a clock? If the second hand is 10 cm long find linear velocity of its tip.
5. The second hand of a watch is 1.5 cm long. Find the linear speed of a point on the second hand at a distance of 0.5 cm from the tip.
6. The extremity of the hour hand of a clock moves 1/20th as fast as the minute hand. What is the length of the hour hand if the minute hand is 10 cm long?
7. Calculate angular velocity of the earth due to its spin motion.
8. A turntable rotates at 100 rev/sec. Calculate its angular speed in rad/s and degrees/s.
9. Propeller blades of an aeroplane are 2 m long. When the propeller is rotating at 1800 rev/min, compute the tangential velocity of the tip of the blade. Also find the tangential velocity at a point on blade midway between tips and axis.
10. The length of an hour hand of a wrist watch is 1.5 cm. Find the magnitudes of following w.r.t. tip of the hour hand a) angular velocity b) linear velocity c) angular acceleration d) radial acceleration e) tangential acceleration f) linear acceleration
11. A turntable has a constant angular speed of 45 r.p.m. Express this in rad per second and degrees per second. If the radius of the turn table is 0.5 m, what is the linear speed of a point on the rim?
12. The linear velocity of a point on the rotating disc is 3 times greater than at a point on the at a distance of 8 cm from it. What is the diameter of the disc. Ans: 24 cm.
13. A disc has a diameter of one metre and rotates about an axis passing through its centre and at right angles to its plane at the rate of 120 rev/min. What are the angular and linear speed of a point on the rim and at a point halfway to the centre.
14. A body rotates in a circular path of radius 0.25 m at 240 r.p.m. Find its angular and linear speeds. If the angular speed changes to 330 r.p.m. in 10 s. Find the angular and linear accelerations.
15. A disc is rotating in a horizontal plane about a vertical axis passing through its centre at 150 r.p.m. When accelerated its speed increases to 1050 r.p.m. in 3 s. What is the angular acceleration caused assuming it to be uniform? What will be the angular velocity of the disc in r.p.m. after 2 more seconds? How many rotations does it makes during this time and what is the angular displacement?
16. The angular acceleration of a body rotating about a given axis is 1 rad/s2. Through what angle does it rotates during the time in which its angular velocity increases from 5 rad/s to 15 rad/s.
17. A disc rotating about an axis passing through its centre and right angles to its plane has its angular speed reduced 50 r.p.s. to 25 r.p.s. at 5 s. How much time does it take and how many revolutions does it make during this time? How much time does it take and how many more revolutions does it make before coming to rest.
18. The angular velocity of a disc rotating in a horizontal plane about a vertical axis passing through its centre increases from 600 r.p.m. to 3000 r.p.m. in 5 s. Find the angular acceleration of the disc assuming it to be constant. What are the initial and final angular velocities of the disc? What is the angular displacement and number of revolutions made by the disc during this time? Find the linear velocity of a point on the rim of the disc if its radius is 0.5 m.
19. A satellite revolves around the earth in a circular orbit of radius 7000 km. If the period of revolution is 2 hours, calculate its angular speed, linear speed and centripetal acceleration.
20. Find the speed at which the point on the equator move as the earth rotates about its axis. Take radius of the earth as 6400 km
21. The tangential acceleration of a particle moving in a circular path of radius 5 cm is 2 m/s2. Angular velocity of the particle increases from 10 rad/s to 20 rad/s during this time. Find the duration of time and number of revolutions completed during this time.

5. 1.05 x 10-3 m/s
6. 6 cm
9. 376.8 m/s, 188.4 m/s.
10. 1.454 x 10-4 rad/s, 2.182 x 10-6 m/s, 0 rad/s2, 3.171 x 10-10 m/s2, 0 m/s2, 3.171 x 10-10 m/s2.
11. 4.71 rad/s, 270 degrees/s, 2.355 m/s.
12. 12.57 rad/s, 6.28 m/s, 12.57 m/s, 3.14 m/s.
14. 31.42 rad/s2, 1650 r.p.m., 45 rotations.