NYJC_EJC 2026 Rotational Motion Tutorial 1

Page 1 Tutorial 1 - Rotational Kinetics and Moment of Inertia Rotational Kinetics 1 When a slice of buttered toast is accidentally pushed over the edge of a counter, it rotates as it falls. If the distance to the floor is 76 cm and for rotation less than 1 rev, what are the (a) Smallest angular speed and (b) largest angular speeds that cause the toast to hit and then topple to be butter-side down? 2 A flywheel turns through 40 rev as it slows from an angular speed of 1.5 rad s-1 to a stop. (a) Assuming a constant angular acceleration, find the time for it to come to rest. (b) What is its angular acceleration? (c) How much time is required for it to complete the first 20 of the 40 revolutions? 3 Starting from rest, a wheel has constant a = 3.0 rad s-2. During a certain 4.0 s interval, it turns through 120 rad. How much time did it take to reach that 4.0 s interval? 4 A seed is on a turntable rotating at 33.3 rev/min, 6.0 cm from the rotation axis. What are (a) the seed’s acceleration and (b) the least coefficient of static friction to avoid slippage? (c) If the turntable had undergone constant angular acceleration from rest in 0.25 s, what is the least coefficient to avoid slippage? 5 In the figure, wheel A of radius rA = 10 cm is coupled by belt B to wheel C of radius rC = 25 cm. The angular speed of wheel A is increased from rest at a constant rate of 1.6 rad s-2. Find the time needed for wheel C to reach an angular speed of 100 rev/min, assuming the belt does not slip.

Page 2 Moment of inertia 6 (a) Calculate the moment of inertia of a thin circular solid disk about an axis that go through its centre perpendicularly to the disk. The disk has a mass M and radius R. (b) Calculate the moment of inertia of a uniform solid cone about an axis through its center. The cone has mass M and altitude h. The radius of its circular base is R. 7 (a) Calculate the moment of inertia of a uniform solid block with edge length, a, b and c about an axis through its centre of mass and perpendicular to the large faces. (b) The uniform solid block has mass 0.172 kg and edge lengths a = 3.5 cm, b = 8.4 cm, and c = 1.4 cm. Calculate its rotational inertia about an axis through one corner and perpendicular to the large faces.

Page 3 Answers 1 (a) 4.0 rad s-1 (b) 12.0 rad s-1 2 (a) 335 s (b) - 4.5 × 10-3 rad s-2 (c) 98 s 3 8.0 s 4 (a) 0.73 m s-2 (b) 0.074 (c) 0.11 5 16 s 6 (a) 𝐼 = 1 2 𝑀𝑅2 (b) 𝐼 = 3 10 𝑀𝑅2 7 (a) 𝐼𝐶𝑀 = 𝑀 12 (𝑎2 + 𝑏2) (b) 4.7 × 10-4 kg m2