A horizontal disk with a radius of 10 cm rotates about a vertical axis through its center. The disk starts from rest at t = 0 and has a constant angular acceleration of 2.1 rad/s2 . At what value of t will the radial and tangential components of the linear acceleration of a point on the rim of the disk be equal in magnitude?
a. 0.55 s
b. 0.63 s
c. 0.69 s
d. 0.59 s
e. 0.47 s
[Ques. 2] A wheel (radius = 0.20 m) starts from rest and rotates with a constant angular acceleration of 2.0 rad/s2 . At the instant when the angular velocity is equal to 1.2 rad/s, what is the magnitude of the total linear acceleration of a point on the rim of the wheel?
a. 0.40 m/s2
b. 0.29 m/s2
c. 0.69 m/s2
d. 0.49 m/s2
e. 0.35 m/s2
[Ques. 3] A disk (radius = 8.0 cm) that rotates about a fixed axis starts from rest and accelerates at a constant rate to an angular velocity of 4.0 rad/s in 2.0 s. What is the magnitude of the total linear acceleration of a point on the rim of the disk at the instant when the angular velocity of the disk is 1.5 rad/s?
a. 24 cm/s2
b. 16 cm/s2
c. 18 cm/s2
d. 34 cm/s2
e. 44 cm/s2
[Ques. 4] A wheel rotates about a fixed axis with a constant angular acceleration of 4.0 rad/s2 . The diameter of the wheel is 40 cm. What is the linear speed of a point on the rim of this wheel at an instant when that point has a total linear acceleration with a magnitude of 1.2 m/s2?
a. 39 cm/s
b. 42 cm/s
c. 45 cm/s
d. 35 cm/s
e. 53 cm/s
[Ques. 5] A wheel rotating about a fixed axis with a constant angular acceleration of 2.0 rad/s2 starts from rest at t = 0 . The wheel has a diameter of 20 cm. What is the magnitude of the total linear acceleration of a point on the outer edge of the wheel at t = 0.60 s?
a. 0.25 m/s2
b. 0.50 m/s2
c. 0.14 m/s2
d. 0.34 m/s2
e. 0.20 m/s2
[Ques. 6] A wheel rotating about a fixed axis has a constant angular acceleration of 4.0 rad/s2 . In a 4.0-s interval the wheel turns through an angle of 80 radians. Assuming the wheel started from rest, how long had it been in motion at the start of the 4.0-s interval?
a. 2.5 s
b. 4.0 s
c. 3.5 s
d. 3.0 s
e. 4.5 s
[Ques. 7] A thin uniform rod (length = 1.2 m, mass = 2.0 kg) is pivoted about a horizontal, frictionless pin through one end of the rod. (The rotational inertia of the rod about this axis is ML2/3.) The rod is released when it makes an angle of 37 with the horizontal. What is the angular acceleration of the rod at the instant it is released?
a. 9.8 rad/s2
b. 7.4 rad/s2
c. 8.4 rad/s2
d. 5.9 rad/s2
e. 6.5 rad/s2
[Ques. 8] A wheel starts from rest and rotates with a constant angular acceleration about a fixed axis. It completes the first revolution 6.0 s after it started. How long after it started will the wheel complete the second revolution?
a. 9.9 s
b. 7.8 s
c. 8.5 s
d. 9.2 s
e. 6.4 s
[Ques. 9] A wheel rotates about a fixed axis with an initial angular velocity of 20 rad/s. During a 5.0-s interval the angular velocity decreases to 10 rad/s. Assume that the angular acceleration is constant during the 5.0-s interval. How many radians does the wheel turn through during the 5.0-s interval?
a. 95 rad
b. 85 rad
c. 65 rad
d. 75 rad
e. 125 rad
[Ques. 10] A wheel rotates about a fixed axis with an initial angular velocity of 20 rad/s. During a 5.0-s interval the angular velocity increases to 40 rad/s. Assume that the angular acceleration was constant during the 5.0-s interval. How many revolutions does the wheel turn through during the 5.0-s interval?
a. 20 rev
b. 24 rev
c. 32 rev
d. 28 rev
e. 39 rev
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