A solid circular disc m , R translates with v 0 and rotates with ω 0 = 2 v 0 R , at t = 0 . Because of friction, pure rolling starts at t = t 0 . The coefficient of friction is μ k . Find t 0 .

The frictional force provides the torque required for pure rolling motion(Torque is being calculated around an axis passing through the centre of the disc) τ = r × f ⇒ τ = f r sin θ here θ = 90 ° τ = f r We use the maximum value of friction possible here τ = μ k m g r Now torques can also be written as τ = I α So, - I α = μ k m g r .........(1) Here negative sign represents the retarding nature of the torque due to friction For a disc, the moment of inertia around an axis passing through its centre is m r 2 2 Using in equation (1) - m r 2 2 α = μ k m g r ⇒ α = - 2 μ k g r Let us assume, the velocity of the centre of disc when pure rolling has begun i.e. at time t o is v . Along the horizontal direction the only force acting is that of friction, thus: m a = f ⇒ m a = μ k m g ⇒ a = μ k g Here a Is constant and hence we can use v - u = a t ⇒ v - v o = μ k g t o ⇒ v = v o + μ k g t o Since there is a constant angular acceleration α = - 2 μ k g r We can use ω - ω o = α t ⇒ v r - ω o = - 2 μ k g r t o ⇒ v o + μ k g t o r - 2 v o r = - 2 μ k g r t o ⇒ v o + μ k g t o - 2 v o = - 2 μ k g t o ⇒ - v o = - 3 μ k g t o ⇒ t o = v o 3 μ k g

EASY

JEE Main/Advance

IMPORTANT

Earn 100

A disc of radius $R$ has linear velocity $v$ and angular velocity $ω$ as shown in the figure. Given $v = R ω$ . Find speed of points $A, B, C, D$ on the disc.

Important Questions on System of Particles and Rotational Motion

EASY

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Physics>Chapter 6 - System of Particles and Rotational Motion>EXERCISE 6.9>Q 53

A wheel rolls purely on ground. If the velocity of a point ' $P$ ' as shown on periphery of a body has a velocity equal to the velocity of the centre of mass of the body. Then $θ =$ ?

Question Image

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Physics>Chapter 6 - System of Particles and Rotational Motion>EXERCISE 6.9>Q 54

A solid circular disc $(m, R)$ translates with $v_{0}$ and rotates with $ω_{0} = \frac{2 v_{0}}{R}$ , at $t = 0$ . Because of friction, pure rolling starts at $t = t_{0}$ . The coefficient of friction is $μ_{k}$ .

Question Image

Find $t_{0}$ .

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Physics>Chapter 6 - System of Particles and Rotational Motion>EXERCISE 6.9>Q 54

Question Image

Find velocity of centre of disc at $t = t_{0}$ .

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Physics>Chapter 6 - System of Particles and Rotational Motion>EXERCISE 6.9>Q 55

A solid sphere, a disc and a solid cylinder all of same mass and made of same material are allowed to roll down without slipping, from rest, down an inclined plane. Then

EASY

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Physics>Chapter 6 - System of Particles and Rotational Motion>EXERCISE 6.9>Q 56

A solid cylinder rolls without slipping down a rough inclined plane without slipping as shown in figure. Choose the correct statement from the following.

Question Image

MEDIUM

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Physics>Chapter 6 - System of Particles and Rotational Motion>EXERCISE 6.9>Q 57

A cylindrical rod of mass $M$ , length $L$ and radius $R$ has two cords wound around it whose ends are attached to the ceiling as shown. The rod is held horizontally with the two cords vertical. When the rod is released, cords unwind the rod rotates. Find tension in the cords as they unwind.

Question Image

EASY

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Physics>Chapter 6 - System of Particles and Rotational Motion>EXERCISE 6.10>Q 60

A solid sphere rolls without slipping on a rough horizontal surface under the action of a constant force $F$ applied as shown. The nature and direction of friction are

Question Image

EASY

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Physics>Chapter 6 - System of Particles and Rotational Motion>EXERCISE 6.10>Q 61

The rigid body is a thin circular wheel and the force is applied at the centre as shown in figure. The force of friction acting on the wheel is

Question Image

A disc of radius R has linear velocity v and angular velocity ω as shown in the figure. Given v=Rω. Find speed of points A,B,C,D on the disc.

Important Questions on System of Particles and Rotational Motion

Learn and Prepare for any exam you want !

A disc of radius $R$ has linear velocity $v$ and angular velocity $ω$ as shown in the figure. Given $v = R ω$ . Find speed of points $A, B, C, D$ on the disc.