MCQs: Angular acceleration
1. An unbalanced torque acts on a disc that is at rest. After 5 s the disc is rotating at 2 revolutions per second. How many revolutions has the disc made
ωi = 0 rad s-1
ωf= 4π rad s-1
t = 5 s
θ = (ωi + ωf)t/2 = 4π x 5 /2 = 10 π = 5 revs
2. An unbalanced torque causes a disc rotating at 2 rad s-1 to accelerate at 4 rad s-2. How many rotations will the disc make in 5s?
θ = 2 x 5 + 1/2 x 4 x 52 = 60 rads = 60/2π revs
3. The wheels of a car are rotating at 4 rev s-1 . The brakes cause the wheel to stop rotating after 6 rotations. The time taken to stop the wheel is.
ωi = 4 x 2π rad s-1
ωf = 0 rad s-1
θ = 6 x 2π rads
θ = (ωi + ωf)t/2
t = 2θ/(ωi + ωf) = 24π/8π = 3 s
4. A wheel is pushed with a constant unbalanced torque so that it acheives an angular velocity of 20 rad s-1 in 5 s. Calculate the angular acceleration.
α = (ωf - ωi)/t = (20 - 0)/5 = 4 rad s-1
5. A wheel rotating at 4 rad s-1 is accelerated to 12 rad s-1 after rotating 32 rad. The angular acceleration is.
ωf2 = ωi2 + 2αθ
α = (ωf2 - ωi2)/2θ = (122 - 42)/64 = 2 rad s-2
6. The graph below represents the angular motion of a body.
The number of revolutions made in 10 s is.
from graph angle = 20π = 10 revs
7. The graph below represents the rotation of a rigid body
The angular acceleration of the body is
constant gradient implies constant velocity
8. The graph below represents then rotation of a rigid body
The angular displacement of the body in 10 s is
Displacement = area under graph = 1/2 x 20 x 10
9. A mass moves in a circle on the end of a 20 cm long string. If the tangential velocity is 20 m s-1 how many cycles will it complete per second?
circumference = 2πr = 2π x 0.2 = 0.4π
time for one rev = cirumference/speed = 0.4π/20 number of cycles per second = 20/0.4π = 16
10. An unbalanced torque causes the body shown to rotate about point A.
If the rotational acceleration of point Y is 9 rad s-2 the angular acceleration of point X will be.
all points on a rigid body have the same angular acceleration